This visit into the minds of Elena and Damon begins after the end of Season 4, Episode 17, Because the Night...
Elena
"I wish this could have gone differently," Elena had told Damon as she left in his car with Rebekah, "I really do."
And she really did, she did wish it. Despite his current disagreements with her, despite his attempts at manipulation, she still wanted to be with him.
Despite his denials, she knew he was just like she was now. Nearly everything he said showed it. Certainly his telling of how manipulated Lexi was evidence of it, his reactions when Lexi returned to Mystic Falls. What was she supposed to think? She had tried to talk to him about it, but he wouldn't listen.
She didn't trust Rebekah, she had been betrayed by the Original too often. But now it seemed they were on the same side – she didn't want the cure, but Rebekah did, or said she did. Elena didn't understand why the blond vampire would want to be cured – it made no sense to her, so she really couldn't completely trust the Original. And really, Elena hadn't been able to handle Damon on her own – Rebekah had to come to her aid.
So Elena couldn't trust Rebekah, but she could work with the Original to get the cure – get the cure and keep it from herself.
The only bad thing in all of this was leaving Damon, but she knew Damon well enough to know that he would find her again. That was one thing Damon had always done, something he always would do.
And when Damon did find her, things would be different. There would be no cure to fight over, there would be no reason for him to try to force it on her. Then he would see what she could see now, that they were exactly alike. He would see that she and Damon should be together.
Damon
Damon had failed Elena before, but this time seemed like the worst. His failure was complete. She was with an Original who hated her, going to Katherine. Katherine, who would do anything she had to do to get what she wanted – to the point of sacrificing Jeremy. Elena was going to Katherine, whose actions had led to him forcing Elena to "flip the switch".
Damon had failed Elena, though she wouldn't see it that way. The way she was now, she only saw him as an impediment, something in her way. She couldn't understand that she might someday want to flip the switch again, that she might someday want her humanity back. She couldn't believe that, no matter how often he told her.
He understood her attitude. He had been there himself. It had taken something remarkable for him to want to turn his humanity back on. She never knew what it took for him to do that for her, never appreciated it. And, it appeared to him, that, despite her claims to always love him, he couldn't get her to turn her humanity back on for him.
At least he couldn't get her to do it for him yet. He wasn't giving up on her.
He still loved her, still wanted her. That fact that she wasn't fooled by his attempts to manipulate her only made him respect her more, want her more. It only proved how remarkable she was - the opposite of Stefan's Lexi.
So he had to find her again, had to keep her from doing something she would regret. He had to get his car back anyway.
And at the same time, he had to somehow avert the apocalypse that Stefan had let happen. He had to save his brother, Caroline and Bonnie so that if he ever did get Elena to turn her humanity back on, she would want to keep it.
All of this for a girl who, for now anyway, only thought of him as an impediment. Would he have done the same for Katherine? For anyone else?
Damon didn't think about that for very long, it didn't matter. He was still alive, and so was Elena; and since they were both alive, he would do what he had always done since he came to care about her. He would find her and protect her – and somehow avert an apocalypse in the process.
Oooh, Caroline is now a mass murderer, as well as an Elena-betrayer and judger. No wonder Stefan's always talking to her – they are as alike as Elena and Damon…(not that we want to see Stefan/Caroline smoochies - please no…please have some pity for us…)