That connection is something that’s clearly very primal and fundamental to Steve, something that I would argue Steve feels makes up a key part of who he is. In CA:TFA, the first time in the whole movie you see real panic on Steve’s face is when that train door slams closed between him and Bucky, suggesting he considered that moment more frightening than, say, being used as a test subject by the U.S. Government. There’s no truly logical reason why Steve didn’t give Peggy his coordinates just before the last crash, but it’s hard to ignore the possibility that, at that point, he didn’t want to be found.
There are also several instances throughout both movies where Steve calls forth incredible violence for Bucky’s sake - up until the moment that the Winter Soldier crashed their car, snippets of conversation made it clear that he was still thinking of SHIELD in terms of salvage. Once he realized what they’d done to Bucky, however, he would accept nothing less than their complete and utter destruction. In CA:TFA, the man who “didn’t want to hurt anyone” burned through HYDRA’s HQ without mercy because they were the reason Bucky was “dead.” When he’s dealing with someone who’s hurt Bucky, one of the most basically decent Avengers loses every ounce of his fairness or mercy.
Because, when someone attacks such a core part of you, it becomes a battle of life and death. I’ve written
before about how the rest of the team might be upset that they’re not being factored in Steve’s head, but the truth is that choosing Bucky is so fundamentally a part of who Steve is as a person that to do otherwise would be in direct opposition to Steve’s core identity. We’ve talked about how Steve seems to have no sense of self-preservation, but his protection of Bucky echoes that primal fight for survival in several ways. You could argue, then, that Steve sees his relationship with Bucky, or the person that he is when he’s with Bucky, as his true “self.”
And to protect that, he’ll do whatever he has to. No matter who or what gets in the way.
