Because I am a masochist, I rewatched the part of s5 e3 where Klaus goes to Elijah to beg him to help Hayley. While I don't like most of the season, there are some gems in there, especially wrt Klelijah. Also, this kind of ties in with the idea of unconditional love, which @kylermalloy talked about in this great post.
In a sequence mirroring the first episode, Klaus pleads Elijah to come back with him. But the way he goes about it is just so... wrong?
First, he says evokes the vow, and says that Elijah is shirking his responsibilities. When Elijah doesn't respond as expected, he tries to convince Elijah that he loved his family. That Elijah loved Klaus, that Elijah loved Hayley (relying on Elijah’s unconditional love which he denied for so long) . Elijah responds basically by saying, “I don't give a shit”. This is partly due to his amnesia, but also, as he reveals later, because he has learned about the Mikaelsons and his own role in it, how Elijah Mikaelson constantly sacrificed his own happiness for the sake of Klaus and the others.
He says: that's not me. I will not sacrifice the happy life I am leading, where "I am truly, truly loved", for your sake. It's a refusal, but he is also giving an opening here, which Klaus completely misses.
Klaus response is: Ah, but you were not unhappy, because we basically ruled the world! And we will do so again! He equates happiness with power. Except... Elijah just told him: I am happy in this little town in the middle of nowhere playing the piano and being with a woman I love and who most importantly, LOVES ME BACK.
So, I think the conundrum here is that the one thing which could have convinced Elijah to return is something Klaus has been incapable of saying for the last four seasons: I love you.
To assure Elijah that it wasn't just continuous sacrifice on his part, that they all loved him in return. That Klaus loves HIM. That Hayley loves HIM. And Rebekah, and Freya. And Hope. That he was part of the family he so desperately tried to save. That they left him alone all these years especially BECAUSE they wanted him to be happy. That saving Hayley and being happy aren't mutually exclusive. But because Klaus is Klaus, he doesn't get this, and Elijah rightfully draws the conclusion that Klaus only cares for him when he needs Elijah to do something for him.
Also, in the same scene Elijah makes this face:
just before he rips out Klaus' heart metaphorically by saying: "Elijah Mikaelson is dead"
And it looked so familiar, and then I realized that in the very first ep Elijah appears in, he makes this face just before he beheads Trevor:
And its the same indulgent smile. He already made up his mind. It doesn't matter what the other party is saying, so he'll just smile, he'll go along, just before delivering the final blow. "Elijah Mikaelson is dead", he says, but Elijah Mikaelson is right there. Except this apathy has never before been directed at Klaus.