Postmodernism, as you've hopefully figured out by . The same is true of the self. Postmodern thinkers tend to see the self as a fluid, ongoing "process" rather than a "being" or a "soul." This means abandoning Descartes's belief in a solid, unquestionable ego (embodied in his cogito, "I think, therefore I am"). You could argue this questioning of the "solidity" of the self, meaning the idea that we are always the same, independent person, began with John Locke back in the Enlightenment. He argued that it was memory that gave us a sense of personal identity, making the self something like an ongoing string of experiences.
Similarly, the postmodern understanding of the individual is all about how we constantly change, and can't separate who we are from the social and linguistic structures that shape our thinking. The person is "fragmented," or "socially-constructed," or a "subject of language," and so on ... Some postmodernists even argue that we all have multiple personalities! Here is a good, slightly goofy but clear explanation of this skeptical attitude toward simple ideas related to identity.
I'd like you to think about this, first in terms of yourself, and then in term of Captain America and Bucky in the film. Do you feel like you are a "thing," that you have a solid set of characteristics that make you "essentially" and "objectively" you? Or do you feel like the self is something complex and confusing, and identity categories really can't define us since we are always changing? Then consider the Captain, who misses a huge era of the world's development and is forced to completely change much of his simple, "modernist" black and white worldview. What holds him together as a person? Is he the same person he was at the beginning by the film's end? And how about Bucky, separated from his memories themselves and controlled directly by outside forces. Who is Bucky, now? Are Bucky and the Winter Soldier the same person or two different people? (In the trailer for Captain America III, Bucky says "I don't do that anymore" - not "it wasn't me who did those things" - worth considering). Write a paragraph responding to these questions by giving your theory of what identity is, with examples.
Also, a paragraph is four sentences minimum, and none of those can be filler or repetitive if you're writing that little. I'm not going to give credit for lame answers that don't engage critically with these questions, or at least show an effort to do so.