Just a question to do with Snape's memory...

I agree with BH and LN.

You're outside, reading, when you hear the voices of a group of kids that give you nightmares and you get up to leave. But not soon enough, they catch you and this time they decide to be even worse, instead of just being hurtful, they embarrass you in front of the whole school, in such a way that you know everyone, in every house will be talking about it.

Then you hear Lily, the girl you've been thinking about lately show up, and you can hear the slight humor in her voice, even asshe's spending so much time trying to talk her house members into letting you down.

And you're finally let down, and Lily is still talking with James and her house members, not coming to your side, not fighting them, and it only points out the very thing you were worried about happening when Lily first got sorted into her house, she was on their side, with them.

When she finally deigns to notice you, all that emotion bursts forth. And you rage at her, because betrayal by those you love, is so much worse than that of people that you don't know.

And, because of their past relationship, it was harder to forgive that one moment that exploded between them.

Severus Snape grew older, and began to try and atone for his mistakes. I hope, that if Lily had survived, that she would have attained enough maturity to accept his atonement, and maybe made a little atonement of her own.

If James Potter had not put him in that situation, he would never have called Lily a mudblood. Think about it...

You're a boy, you're being publicly humiliated yet again by your most hated enemy, and you're saved by a GIRL. That's just as bad as what your enemy is doing to you, it just compounds the humiliation.

And Lily shot right back at him with a biting insult of her own! Funny how no one seems to remember that...

I think it would be more humiliating if he was helped by a girl. He would like to prove that he was better than James, and Lily doesn't quite help, by trying to help him.
And 'mudblood' was obviously the first bad thing he could think of.

I agree with what BlackHound said. I would add this extra point :

The scene must have been witnessed by other students, some of them from Slytherin. Severus tried to play it the pure-blood (while he's only a half-blood), he was already treading a fine line in this regard. His friendship with Lily must have already looked suspicious in Slytherin. He did not wish to look even more Muggle-friendly than he was already by showing some respect to her in public. He had to play it the "racist pureblood" to stand a chance in front of Slytherin later. Not an easy situation to find oneself between a rock and a hard place. Poor Severus...

I think he lashed out at her because he had been attacked and was being publicly humiliated by his worst enemy and the one and only friend he had's first reaction was to start to laugh at him. Harry himself noticed that Lily looked like she was about to laugh before she caught herself and started telling James off. And on top of that while Snape was hanging upside down, exposed to everyone, James and Lily were basically arguing as to why she wouldn't go out with James. Snape would have been feeling scared, humiliated and betrayed by Lily when he lashed out at her.