Point one: Snape originally stayed in love with Lily because of the lost chance. He actually did think he had a shot with her till he called her a mudblood, but Harry pointed out that in fact he never did. I mean some people fall in love and if their loved one dies, never date again, so I was assuming Snape's feelings were of that variety. He knew they weren't actually "dating" but he thought he'd had a chance before That Day. Now, Harry tells him "Sounds like this Guy never had a chance with that Girl ever, because she's shallow." So, yeah, hearing that he's held on to these feelings for no reason instead of "if only I'd not called her a mudblood we'd have married" - I can see how hearing that you've really wasted your past 11 years of life can piss you off. His rage was due to changing his mind, but clearly Snape finds it hard to Not Shoot The Messenger.

Point two: It's more that Dumbles probably had been insisting for years (in a more subtle way than I'm about to do) that Loving Lily made him a better person so he should continue to do so. But the axiom for Loving Lily - that he could possibly have been with her if he'd been a better person in the first place - has indeed shattered. I don't think he's mad b/c Lily was shallow specifically, but just that she never, ever, ever, would have been with him. So yeah, he's trying to update on that new axiom.

Point three: as others have said, Snape Loves Lily is canon, but if you take that axiom above, it's not quite that unrealistic. I knew a girl in college who didn't date for 4 years after her boyfriend was killed in a car accident. And remember Snape thinks it's his fault she died, too.