Well, there are several reasons in my opinion.
1. Damon has tried to kill BOTH of her best friends. There was Caroline, while they were dating, and also he basically used her as his own personal blood bank. Then there was Bonnie in History Repeating. Plus, he has threatened them both MULTIPLE amount of times. That for one, would make me dislike him. (And, in Brave New World, he's going to try and kill Caroline again)
2. He tried to kill Jeremy. Now, I'm not Elena, but I'd NEVER forgive anyone that tried to harm my younger sister or brother, much less tried to KILL them. I mean, she loves her brother right? So why the HELL would she be with a guy that tried to kill him?
3. Damon's killed more people than he's saved. Let's review: there's the two in Pilot, Coach Tanner, the boy in 162 Candles, and ALL the people in the graveyard in You're Undead to Me (like 5 right?). And he has saved... Elena and Caroline. While he did save her, it doesn't make up for all the innocent people's lives he has taken. And another thing, WHO KNOWS how many people he killed before he came to Mystic Falls.
4. Damon COULDN'T tell the difference between Katherine and Elena. And Stefan did. Simple as that. It just proves that he was using Elena as a substitute for Katherine, or else he would have known the difference. Stefan truly loves Elena, and therefore was not fooled by Katherine's games.
5. AFTER Katherine rejected him, he went to Elena. Not before, but after. There's no other way to put it other than she was his backup plan; the girl to run to if the first one didn't work out. And Elena doesn't need someone who puts her second-best.
6. People say Stefan and Elena are cliche? DAMON and Elena are cliche. Seriously, how many times have we seen the bad guy get the girl? It happens more often than not now adays, and is really repulsive to see over and over and over again. In almost every show there is a good girl and bad boy, or vise versa. Very stupid, very annoying, and VERY cliche.
7. Stefan and Elena have a deeper connection than Damon and Elena. Delena are purely attraction and lust. Damon is attracted to Elena because she looks exactly like Katherine, who he is STILL obsessed with in my opinion. And Elena is attracted to Damon because he's sexy (lets admit it, Ian Somerhalder is FINE). But there's nothing else; not love, but lust (and I'm not entirely sure that Elena is lusting after him that much).
8. Elena isn't Katherine, and she doesn't seem like the type to cheat. She loves Stefan, and is with Stefan, and it would be OOC for her to cheat on him with Damon. Unlike Katherine, she doesn't toy with the boys' emotions, and wouldn't string them both along. And she's already said it will ALWAYS be Stefan.
I'm sure there are more out there, and I KNOW I can come up with more reasons, but I'm on a press for time, and this is all I can write for now. I don't expect Delena fans to agree with me, but then again, why would they be here? ;)