Dean: How could I? All you’ve ever done is run away.
Sam: And I was wrong. Every single time I did.
Here's Dean, planning on saying 'yes' to Michael, and being bitchy and resentful to everyone who loves him. His sweeping condemnation of Sam is both sincere and insincere. It the type of over-the-top remark one makes when angry, an expression of feelings one normally keeps to one's self because they are nasty and unfair.
Sam's response sticks with me. It's self-loathing, for one. Not only had Sam done a great many things in his life that didn't involve running away, but he wasn't wrong every time he did. He certainly wasn't wrong to go to Standford.
Maybe, to a certain extent, Sam is making this statement to turn the conversation back to Dean's actions, rather than Sam. Saying whatever it takes to get the conversation back on target. But I don't think that's the whole story...I think at this point in his life, he believes it.
Sam's self-loathing is different from Dean's in some key ways. Sam possesses something - It is almost optimism, something rather like hope - that Dean does not have. In season five, Same feels like a screw-up. But note the past tense in the above quote: Sam says that he was wrong. Sam believes he can change - or at least holds on to the hope that he can.
Sam doesn't believe himself to be screw-up in the sense of being incompetent. Sam is highly competent, and I do not think he doubts that. If nothing else, Stanford is inarguable proof that he has always been more than capable of getting his act together. Rather, Sam's multitude of mistakes are more about morality, emotions, and relationships. He trusts people he shouldn’t trust. He lies to people he shouldn’t have lied to. He runs from people he should have trusted. He has (to quote his hallucination of Dean in Sam, Interrupted) a "black spot on [his] soul". His mistakes aren’t a demonstration of incompetence. They signify, instead, selfishness. Anger. Arrogance. And something evil inside of him. Something inhuman, perhaps.
But they are all "mistakes". Dean's self-loathing, which in later seasons became an end onto itself, does not have room for mistakes. Dean's wrongdoing is simultaneously necessary and righteous, and further proof that he's a terrible person and nothing can be done about it. Dean in his own mind will always be the righteous man who tortured souls in Hell.
Speaking only in terms of the brothers' perceptions of themselves: Sam was awful from infancy - Dean started out good and became awful through his actions, though his definition of "actions" can be broad. Whether we are talking about a young boy's decision to play arcade games for a little while, or an adult man's choice to mindwipe his ex and her young son for no logical reason - it's all the same to Dean. Dean's actions cause his incurable corruption while Sam's bad choices stem from his impurity. Dean does terrible (yet usually righteous) things. Sam makes mistakes.
And here's the thing about mistakes: common wisdom says you can learn from them.
Sam is action boy. He doesn't get bogged down in his mistakes, not generally. Sam does something about it. This is his attitude in all situations. When his brother went to Hell, he did everything in his power to save Dean. Up to and including demanding a demon to put him in Hell in Dean’s stead.
When that failed, he teamed up with a demon his brother hated and started using his own demonic powers as part of a plan to kill the demon responsible for his brother’s death. He even went so far as to start drinking demon blood, something that deeply disturbed him, in order to accomplish his goals. When he reached the point of being suicidal, he didn't just kill himself. He intended to go down fighting Lilith. Sam is stubborn, determined, and willing to do whatever it takes. And if he fails, he’ll go down fighting.
So when season four reaches its close, when it becomes apparent that all of Sam's choices since meeting Ruby have been leading him to the destruction of the world, Action Boy is going to pick himself up, dust himself off, and try to learn from his mistakes. Sam has a very intellectual way of seeing things at times, perhaps to compensate for his poor instincts about people. So he'll pour over his mistakes, trying in his head to pinpoint where he went wrong, all the lousy choices he made along the way from devoted brother to triggering the apocalypse. And, it seems, Sam went back farther: Stanford, Flagstaff, maybe those Lucky Charms he puppy dog eye'd Dean into giving him all those years ago.
So when Dean says, “All you’ve ever done is run away,” Sam doesn’t argue. He already believes it. The people who loved him, the people who had his back, his family he left them. And the only thing that came out of was Jess’ death. He’s screwed up every step of the way - being merciful when he should have been tough, cold when he should be compassionate. He trusted a demon when he should have trusted his family. He betrayed his brother in more ways than he can count.
“And I was wrong. Every single time I did.”
But that was then. This is now. He's been wrong his own life, but now he knows it. He's right now Yeah, he screwed up, and he hates himself for it. But the game isn’t over yet. People can change. Monsters can make choices - can save the world. Sam still has that confidence undimmed, that hope/optimism that will lead him to say "yes" to Lucifer.
“Nothing ever gets wiped,” Sam said in Defending Your Life, and he believes that, too. That’s why he believes he deserves to be in Hell. But even damned, Sam believes he has choices. And his choices matter. Going to Hell becomes his second chance.