I appreciated your essay, I thought it was both thoughtful and reflective given the prompt. As you say, I think the narrative needs a little work. Where you are at your strongest is in your use of abstraction. In particular, the second part of your essay detailing the absence of your father was well done. Where I would make some improvements is the way in which you bring your abstract conceptualization of identity formation into context with your personal narrative. This needs to be much tighter, more focused (especially if there is a word limit). Another way to write an essay like this--and this is just my opinion, you may want to stick with what you have--is to interrogate how the abstract "presence" or "absence" affected you on a personal level. Take a step back from your story and approach it how you might a novel. Think about about how the "character" in your novel is affected by the presence or absence of his father. Then explain why that matters. I've found this approach, at least for me, allows me to analyze how
these two particular issues matter.
Another thought I had was the logic behind the construction of this argument:
If who we are were shaped through the influences of others, then ironically, these others would cease to be differentiated from oneself. But rather, others become the very origin of our identity-in which a coalesce of one's self and others occurs. Therefore one's identity is akin to the influences of others. These influences can never simply exist as white and black. Instead, they exemplify dualistic qualities of both positives and negatives-bleeding into the lightness between the extremities of white and black.
If I understand you correctly, you posit that the process of identity formation is shaped by our interaction with other people. Fair enough. To suggest that your father shaped your life, values, character, etc. is all well and good, but you seem to go further to suggest that your identity and his are inextricably linked. Yet where is the individual in this construction? Do we not have inherent individual agency? In your argument, where does your identity begin and your father's end?
Hopefully this helps you a bit. Good luck with your applications.