Any attempt to understand Sirius, Lily, James, Snape, the relationships (both positive and negative) between them, and yes, even to some extent even McGonagall and Dumbledore ends up pivoting on the events at the end of the 1975-1976 school year when Lily, James and their friends (or enemies as the case may be) were in their fifth year. We do not know the exact chronology, what follows is my best reconstruction.

What Happened

My first instinct is to quote it, the first scene is most of page 278 in the American Kindle Edition, the second scene has key details from kindle location 9426-9519 in the American Edition of the fifth book (it is skimmed over in the seventh, though we are told Harry re-watches it), and the third scene takes up a chunk of page 279 back in Deathly Hallows. Overall there is just way too much of Mrs. Rowling's copyrighted text for me to feel comfortable even block quoting it. So I will summarise what we know. From these two books:

Evidence from The Shrieking Shack¹

• “Severus was very interested in where I went every month,”
• Lupin says that Sirius alone is responsible for telling Snape to go into the tunnel, and how.
• Per Lupin, James found out only later what Sirius had done.
• Per Lupin, Snape believed that James and Lupin were in on Sirius' actions.
• Snape confirms that belief as he reveals himself from under the invisibility cloak.

Snape in the Hospital Wing

Immediately following the events in the Shrieking Shack:

“Sirius Black showed he was capable of murder at the age of sixteen,” he breathed. “You haven’t forgotten that, Headmaster? You haven’t forgotten that he once tried to kill me?”²

The above quote is almost trivial, it is hard to blame Snape for disliking someone who tried to kill him after all. The reason I bring it up is that Snape of all people must know that things are not always as they seem - his entire life since the prophesy has been subterfuge. He of all people must understand the value of forgiveness and second chances - if Dumbledore was not willing to give Snape a chance, then he would not be there to complain. And yet, he is not willing to allow for either in the case of those who have wronged him.

First relevant memory from Snape³

• Lily and Snape are an unknown amount older than when they were sorted. We infer that this is fifth year.
• Mulciber has tried to do something to Mary Macdonald "the other day" that Lily considers proof-positive that Mulciber is "creepy." Whatever he tried to do involved Dark Magic.
• Snape dismisses Lily's concerns saying that Mulciber's actions are funny.
• When dismissing her concerns does not work, Snape tries to redirect the conversation to the failings of James and company.
• Snape immediately focuses in on Lupin's status as a werewolf.
• Lily turns cold when responding. My inference is that Lily disagrees with Snape's bias against werewolves. I am unsure if Lily is truly ignorant of Lupin's status, or if she is pretending to be. It probably does not matter which.
• Lily blushes under Snape's "intense" gaze. More is going on in this conversation than the surface words. I am not incredible at this people reading thing. Is Lily reacting to Snape being attracted to her, or is Lily reacting to the fact that she is attracted to James and Snape has accurately called her on the fact?
• Lily defends James and Co saying "They don't use Dark Magic."
• Lily calls Snape ungrateful, because James saved Snape's life.
• The events where James saves Snape in the tunnel are also refereed to as "the other day".
• Snape claims that James was saving himself, that saving Snape was essentially a selfish act.
• Once Lily states that James is "an arrogant toerag," Snape stops listening to anything she says.

Snape's second relevant memory, Order of the Phoenix version⁴

• It is the Defence Against the Dark Arts OWL written exam.
• James and Snape (minimally) leave the exam with the exam question paper.
• James and Lupin are talking very openly about Lupin's status as a werewolf, yet Lupin after himself saying "His name's Remus Lupin" as a joke answer to "signs that identify a werewolf" tells James to keep his voice down two lines later.
• They settle outside under a tree, and Snape just happens to settle down within hearing distance of his worst enemies.
• James is showing off with a snitch, well aware that there are girls in the area (even if they are not watching, they might see him).
• Sirius is bored.
• Sirius claims he does not need to consult a book to quiz Lupin.
• James spots Snape, who is about to leave the area.
• "Snape reacted so fast it was as though he had been expecting an attack"
• James is faster. He uses two fairly harmless spells. He's still watching to see the girls' reaction.
• James uses a spell to wash Snape's mouth out for bad language. This is undoubtedly fairly cruel.
• Lily to the rescue.
• Lily is very cold at first towards James
• Snape fires off something that draws blood.
• James reacts with a spell that leaves Snape hanging upside down with his underwear on display. The humiliation is no doubt worse because the spell used is one Snape invented.
• Lily's face twitches. I think perhaps she considers this fair retribution for a spell that draws blood. She's hiding that fact from James though.
• Lily insists that James and Sirius end the torment.
• Snape calls Lily a Mudblood.
• Lily turns cold towards Snape and calls him "Snivellus" for the first time, knowing that will hurt him.
• Lily says that James is as bad as Snape. Her reasoning is partly that he tries to make himself look cool, and partly that he hexes people just because he can.
• Sirius interprets Lily's comments as essentially boiling down to James being arrogant.
• James returns to tormenting Snape when Lily storms off.

Snape's Third Relevant Memory⁵

• Snape apologies.
• Lily refuses to hear it.
• Snape says he did not mean to call her Mudblood.
• Lily calls him out for his friends who all want to be Death Eaters. She further claims that Snape wants to be one.
• Snape opens his mouth to deny this, but then closes it without saying anything.
• Snape again tries to protest he did not mean to call her names.
• Lily is having none of it, because he calls other people by the same names.
• Snape has no response.

What does this mean

Looking at the events themselves

I do not doubt that James was in fact fairly arrogant, and that was a barrier to any friendship between himself and Lily. That being said, I do not think that Lily disliked him as much as it sounds. I am not the best at reading people, but I think Harry is worse, and, unfortunately, everything we know is filtered through his perceptions (or in this case lack thereof). Snape is inordinately focused on making sure that Lily sees James in a bad light. Some of that is because [Snap] is aware that James is a rival for her affections.

There are, however, only two real possibilities here.

1. Snape is irrationally jealous of the mere possibility that Lily might like James merely because he (James) is popular. Snape is so irrational about Lily that he actually undermines his own position to reassure himself on this point.
2. To bastardise an overused quote, Lily doth protest too much. In other words, she does show signs of being attracted to James, and Snape, being both jealous and perceptive, picks up on these signs. He does not know how to deal with the fact, and undermines his own position trying to undo something he sees going on.

Snape is ungrateful, though if he truly believes that James was motivated by selfishness, then and only then is that attitude justified. Assume Lupin's account is accurate - James neither knew about nor condoned Sirius' extremely poor idea of a "joke." James then himself risked the fully grown werewolf to save Snape. There are a couple of possibilities:

1. It has been suggested that Snape had been speculating that Lupin was a werewolf for some time prior to the incident. Not only that, but that Sirius was aware that Snape had so speculated. If this is true, Snape went down into that tunnel to investigate a suspected werewolf on the night of a full moon, then blames James and Sirius for the fact that he (Snape) found precisely what he expected.⁶ If this is true, then Snape is both a hypocrite and insanely stupid. It is, however, a cunning plan.
2. Snape had no clue what to expect. He did, however, know that Sirius hates him. He broke school rules because Sirius, who hates him, gave him a clue on how to get Sirius' friend in trouble. Because that does not sound at all like a trap. Whether or not you believe that James was in on it, Snape's behaviour is still insanely stupid. Honestly though, we have no reason other than Snape's irrational hatred to doubt James innocence.

Given that in the first memory, Lily dismisses Snape's werewolf theory as essentially old well worn ground, I believe that the first possibility is more likely. Thus Snape intended to find a werewolf, but did not intended to either be saved, nor need saving. He underestimated the danger involved in a werewolf encounter, overestimated the controls on Lupin escaping restraint, or both. Snape intended to be a hero, exposing a danger to the school at great personal risk. This cunning plan was spoiled by three things. Firstly, in that, as I said, he underestimated the danger and required rescue. Secondly, because that rescuer was his own nemesis, and (according to Snape) in on the whole thing anyway. Thirdly, because Dumbledore insisted on keeping the whole matter quiet, and prevented Snape from actually exposing Lupin. Snape resents the fact that he is denied his moment of glory, and is trying to find ways to ensure that the secret he has promised to keep gets out.

Sure, James hates Snape and vice versa. I doubt the event would have changed things even if both were reasonable rational and mature real-world adults (if such a thing exists). In such a case, however, we would expect Snape to give credit where credit is due, and would call him on it when he fails to do so. In other words, the rational, reasonable thing is to criticise Snape for blaming James for the incident.

We do not know what happened to Mary Macdonald, but Lily insists that it is Dark Magic and Evil (her emphasis). Somehow that is funny but James' actions are unforgivable. Even if I entirely agreed with Snape's reading of events, I see only a difference in target. Since I don't agree with Snape's reading, I see that any offence against Snape is unforgivable, but anything Snape, or by extension his friends, does is justifiable. We call such a person a hypocrite, and generally look down on him or her. This is, however, classic villain behaviour.

Looking at the memories

I have some questions about the memories, in both books.

The presentation

Unfortunately our most detailed account of these events comes from the memories that Snape, a master Occlumens. We know that when Slughorn tried to modify a memory to give to Dumbledore, the result was painfully obvious in a pensieve.⁷ What we do not know is if it was obvious because it was modified or if it was obvious because the modification was crudely done.⁸ Thus we do not know if it is possible that Snape modified these memories or not; we do not know how reliable a witness these memories represent.⁹

The second memory, the one with the most discrepancies (see below), has some partial validation in that neither Sirius nor Lupin deny what happened, on the other hand, Harry only describes what he saw, they did not see the memory themselves. If Snape was smart enough to craft his lies on versions of the truth, if he distorted true memories rather than than inventing things out of whole cloth, Harry may not have included the details that would allow either listener to notice the discrepancies.

The content

There are a few details that raise red flags. Unfortunately, some of them may be a cultural thing, the difference between American schools and British ones.

The first is, as I note above, that the students take the exam paper with them when they leave the OWL exam. Based on my experience of standardised exams, this seems incredibly odd. I know that all of the Hogwarts students take the OWLS at the same time, but we also know that not everyone goes to Hogwarts. As corrupt as that culture is, surely the Wizarding Examinations Authority has had to deal with people buying copies of a test before. Controlling access to the exact exam questions used should carry over to the magical world as well.

Second, as everyone is leaving the exam, we overhear James, Lupin, Pettigrew and Sirius talking. Keep in mind two things, this is Snape's memory. He was close enough to at least subconsciously hear them. The book attempts to account for this by saying that Harry has to strain to hear them, but, the passage describes a "gang" of girls as having just left the boys' group, and then, when they start picking on Snape, we see that a number of students are able to quickly gather. Why are they discussing Lupin's status so openly at all? Why does Lupin joke about answering that question in that way? We see no indication of what volume most of the comments were said at, but it is still very odd that so much was said before Lupin became uncomfortable.

Third, Snape settles down in fairly close range to James and Sirius at all. If this were anything other than a necessary plot device in fiction, this right here would be the single strongest indicator that the memories are fabricated. As someone who has had trouble with school yard bullies, you simply do not relax around them. Snape would have picked anywhere else on the grounds. He would have stayed inside rather than willingly putting himself at risk that way.

On a side note, in his work Toxic, WitandAmbition makes very similar points, but focuses more on Lily and Snape starting further back in time to paint much the same picture.

Looking at the Fall-out

Lily and Snape

Some writers blame Lily for the fact that Snape became a Death Eater, pointing to this incident. If she had forgiven him, her friendship would have given him the strength he needed to resist Riddle's temptations. I honestly disagree, and point to the first of Snape's memories as my proof. If she had forgiven him, he would have remained in denial about the evil nature of the actions that Mulciber and his (Snape's) other Death Eater friends were committing. This would inevitably lead to facing the same temptations to joining Riddle. Snape would then have rationalised things saying that by joining Riddle, he would be in a better position to protect Lily. He would figure that Riddle would spare a Death Eater's family even if she was a mudblood. This would draw Snape deeper and deeper into Riddle's atrocities and soul corrupting influence. You simply cannot be around such people without their evil rubbing off on you.

People criticising Lily are essentially pushing her towards missionary dating. It is not precisely the same situation, but it is close enough. Sure you can find anecdotal evidence that missionary dating works, but in general, it is a bad idea.¹⁰

Secondly, I remain unconvinced that Lily was romantically inclined towards Snape at all. Certainly both Snape and James were both romantically interested in her, both aware of the other's interest in her, and both jealous of the other's perceived advantages. It does not follow that just because Lily was friends with someone who wanted that friendship to be more, that she also wanted that friendship to be more.

Lastly, Alan Rickman may be attractive (at least, I am told he is). He is not however, the definitive rendition of Severus Snape. Lets not read more into the text than is actually there just because you actually like the actor as opposed to the character.

Lily and James

Certainly this event clears the way for Lily to begin dating James. Earlier I speculated that there are two possibilities. Either she is embarrassed about being unable to return Snape's feelings, or she is embarrassed about being called upon her own feelings for James. If the latter, I would have expected Lily and James to get together during their sixth year. We are told they did not do so until seventh year.

A third possibility is that it is some combination of both of the above scenarios. If Lily is attracted to but conflicted about James then we have a rational story towards their relationship during seventh year. Instead of a miraculous about face where she goes from hating him to head over heels in love, she has gradually watched him mature over sixth year, and finally become the man she has been pushing him to be as he embraces responsibility as Head Boy in seventh year. In a sense, this is exactly my point about missionary dating. Lily agrees to date James only after the man she has been attracted to all along makes that change to become someone she can see herself marrying on his own, before she begins their relationship. Only then does she allow herself to act on that attraction by agreeing to go out with him.