"That’s what you do, Damon. You think that you don’t … you don’t deserve something, so, you ruin it. I’m not gonna let you pull that this time. Take the cure with me. That’s how much I know this is real. That’s how certain I am that I’m gonna love you, even after this is all over. Take the cure. Be human with me. We can be together. Grow old together. This doesn’t have to be hard anymore.
There was much said about Damon’s insecurities and their influence on his reactions to Elena asking him to become human and grow old with her together, but I wanted to write that all down in one text.
First of all, Damon didn’t have time to think about himself before, because he was – like always – only focused on Elena and her needs, and he didn’t expect Elena to suggest something like that – especially after he just pushed her away. But Elena understands how Damon "works" and she knows the reasons for his behaviour, and she told him that; Elena realizes Damon’s insecurities and sees that he tries to ruin things because he thinks that he doesn’t deserve her and their happiness together. Damon has been told all of his life and undead existence that he is not worth anything and that nobody can love him, so that he can’t believe that he really is loved. And now, Elena wants to spend her life with him, what is everything that Damon has ever wanted, it is the absolute fulfillment of his dreams, but it makes everything even worse for him, because Damon believes that nobody loves him or wants to be with him, so that he now thinks even more that Elena’s feelings are not real. And his self-esteem is even lower than usually, after he just spent almost two episodes with Klaus (no happy ending for Damon) and Shane (most to lose for Damon by cure) constantly telling Damon that he will lose Elena again. Damon knows that it won’t be all "unicorns and rainbows" and (unlike the others) considers the consequences and thinks about the future after events, and he believes that he will skrew things up anyway, so that he tries to make it easier for Elena by pushing her away. He expects Elena to break up with him sooner or later, and he wants to make her do it earlier, to make her feel less guilty and hurt about it, and to protect her by seeming to care less and keeping his pain to himself.
Damon has always been told that he is a bad guy, and he took the role of the "bad boy", and everybody has always said that he doesn’t deserve to be happy. He has never experienced love and happiness as he does now, and he fears that he will ruin things also for Elena. Damon doesn’t consider himself fitting for a "normal" life, he can’t see himself being "normal", and although Damon and Elena and especially their relationship are – in a good way – not normal at all, they will find their own way of "a normal life" together. But Damon can’t imagine himself to be a good husband and father, he thinks that he is not good for Elena and fears that he would destroy her with him. Damon expects himself to skrew up and ruin everything, and he thinks it better to do that on purpose now, before things get so intense that Elena would be harmed with him. And Damon can’t believe that something that Stefan wants can also be right for himself, because Damon has always been told that he is very different from his brother and that Stefan is much better than him. So, when Elena describes a life that fits Stefan’s wishes, Damon thinks that Stefan’s way can’t be what he himself wants, although the two brothers have their differences AND their similarities. Damon considers Stefan more fitting to have such a life with Elena, what is wrong, because Elena has never wanted something like that with Stefan or anybody else.
Damon has been rejected and hurt, broken and hated all of his existence, and he doesn’t dare to hope that things can also be good for him. He has never experienced anything like what Elena gives him now, and it is too painful for him to even consider hoping for love and happiness for himself. And Damon doesn’t understand why Elena loves him, he even still doubts it, so that he can’t think of a value that he can have for Elena as a human, without any of his vampire abilities. He sees his only usefulness for her in protecting her and keeping her safe, and he considers himself the protector of everybody, so that he needs his supernatural powers to protect his loved ones – even more with everybody else becoming human again. Damon especially can’t bear the thought of losing Elena, but even apart from him being her guardian, he can’t imagine what human Damon could offer Elena. Human Damon was naive and helpless, and Damon can’t see that he would keep the personality, the knowledge and the experiences that he gained even after being cured. I don’t know how old Damon was in the show when his mother died, but apart from her, nobody has ever loved human Damon, while vampire Damon is liked by Elena and became her friend, even without him believing that her love for him is real. Damon is very insecure about his role as a human, and he can’t see his unselfishness and goodness, so that he can’t imagine what Elena would like about him and how she could love him as a human. And saying out loud that Elena will die as a mortal makes that fact more real, and although that is a smaller reason, Damon can’t bear losing Elena, and that made his emotional condition at that time even worse, while all of his emotions about what I described before already affected him immensely. Damon has never really had anything, he never had to fear losing something, but now he has Elena, who means everything to him, and he was confronted with the prospect of the loss of her during an already very emotional moment.
And Damon really wants to spend his life with Elena, and he still misses being human. You don’t go from missing something more than anything else to thinking of it being the most miserable thing ever. Damon declared missing being human while he still struggled to bear his emotions and had no perspective at all, so that he doesn’t think the complete contrary now that he can control himself, knows how to live with his feelings, got closer with his humanity again and is even offered a future together by Elena. Damon is fine with Elena "either way", he doesn’t care what she is, because he loves who she is, and he also wouldn’t mind being with her in her 90’s or whatever. But Damon is afraid to lose Elena, when she becomes human again, although he none the less supports her in finding the cure. Damon wants himself and Elena to be human together and grow old together, but he fears losing her; he is honest (except for pushing Elena away to hide his true wishes) in telling Elena that he doesn’t want her to be cured, and he is also – again like always – extremely selfless in still helping her. Damon wants Elena to be happy and safe and things to be real for her, and as long as that is given, he does what he can to give her what she wants – without any thought about himself and his happiness and safety.
But Damon doesn’t want Elena to know about his suffering, so that he couldn’t face her, while pushing her away, because she would have seen the truth in his face, as tears came to his eyes. Damon’s insecurity and pain could already be seen for a long time, it was also obvious shortly before, when Delena were kissing and hugging in the forest; just compare Damon’s faces during the hug in 4x12 (when he put everything aside and was just happy to be with Elena again – and that she was also happy to see him) and this one. Damon hides his true wishes from Elena and tries to skrew everything up, but she understands and knows Damon, she won’t let him ruin things, and she will continue fighting for their mutual true love, what is exactly what Damon had always needed.
But Elena being so close to him and telling him how real her feelings are for her and how deeply she loves him, what is exactly what Damon desires, makes everything harder and more painful for Damon, because he can’t believe – or (to be more accurate) doesn’t dare to believe – that Elena’s love for him is real, and her being that loving and that certain only increases his doubts about its truth. We all know that Elena’s feelings are real, and it just needs to be pointed out again that Elena, who has never wanted to discuss her plans for a future together, who couldn’t bear Matt talking about it, and who couldn’t – after the first phase after her parents’ death when she feared losing everybody – give more than a "for now" to Stefan, that this Elena wants to forever be with Damon, spend her whole life with him and grow old together with him – what she has never desired (or even wanted to discuss) with anybody else. It is a deep commitment, and although Elena has thought about such a future for a very long time, she hadn’t found the right person for her to share such a life with, until she now found the one for her to stay together with forever. And it also needs to be said that Damon, although he couldn’t bear to continue the conversation, didn’t "lash out" after being confronted with his emotions. He didn’t leave to kill some people or sleep around or something like that, what he would have done before Elena brought out the best in him.
So, Damon is afraid and insecure, what explains his reactions, but Elena knows and understands him, she won’t allow him to push her away and destroy their relationship, and she will fight for their true love.