A little of anything and everything. But mostly Tom Hiddleston.
Let me get one thing straight before I get to my point: Sam did not disown Dean.
He’s established distance between them, sure, because he doesn’t think “we’re family” should be a valid excuse for Dean to do whatever he wants. So he’s stepping back from that close, brotherly relationship until Dean proves he can be trusted not to use that relationship to hurt Sam. They are still living together and hunting together, which means Sam is giving Dean a chance to prove himself and repair their relationship.
And yes, it’s important to acknowledge “Sam is giving Dean a chance, he certainly doesn’t have to do that.” Very important.
But it’s even more important to acknowledge that Sam is actually giving Dean multiple chances, chance after chance after chance. Sam gives Dean a chance on the bridge to apologize but Dean walks away. Sam goes with Dean at the end of “Sharp Teeth,” giving him a chance to try to work things out once more. He stays after “The Purge,” even when Dean not only refuses to apologize but says he’d do it again. He goes to his room but doesn’t leave in “Captives.” In “Thinman,” Dean has apparently been hanging around the bunker thinking “up is down” and apparently not thinking about why Sam may be upset with him at all. And Sam waits, still.
There are people saying Sam’s waiting is what they blame him for—that he should sit Dean down and spell things out to him. I’m not sure how well that would work—Dean has steered things away every time Sam tries to talk, and Dean has been talking over Sam’s perspective for years now, twisting things to get his own way (“The Mentalists”). Maybe they could have this conversation, but I doubt it. This seems to be a conclusion that Dean needs to come to for himself.
And Sam is still waiting. Sam has so much faith in his brother, has so much faith in the value of their relationship, that he is waiting, that he is easily acquiescing another chance every time, because he believes it will be worth it.
This isn’t someone who wants out of a relationship. This is someone who has so much faith in this relationship that, even though it has greatly hurt him, he knows that it can be better and what they both need. This is someone willing to give chance after chance because he has so much faith in this relationship and in Dean, because he knows Dean is capable of being a better person and treating him right.
Sam Winchester hasn’t given up on their relationship, not by any means. Sam seems to be willing to give Dean infinite chances, but the act of fixing this relationship is in Dean’s hands now.