Sam: You don't have to trust Redwing. But I'm going to go see if he right. 'Cause I have a feeling they might be part of the Big Three.
Bucky: What Big Three?
Sam: THE Big Three.
Bucky: What Big Three?
Sam: Androids, aliens, and wizards.
Bucky: That's not a thing.
Sam: That's definitely a thing.
Bucky: No, it's not.
Sam: Every tine we fight, we fight one of the three.
Bucky: So who are you fighting now? Gandalf?
Sam: How do you know about Gandalf?
Bucky: I read The Hobbit...in 1937 when it first came out.
Bucky: I got a vibranium arm. I can take them.
Sam: And I can fly, who gives a shit? Wait.
Chosen answer: The sleeve probably would have been ripped to shreds in battle anyway. He was just saving time by ripping it himself. Also, gunfighters would take off their coats in a duel or an arm wrestler rolling up his sleeve.