How would you benefit from and contribute to such an environment?
So, this is the question you are supposed to be answering. Your narrative anecdote, while entertaining, doesn't seem to do this very well, though to your credit you do try to make it relevant at the very end of your essay. However, your actually answer to the first part of the question doesn't show up until your last paragraph, and it is this:
It will allow me to expand my education
A university will allow you to expand your education? Remarkable! You have to be able to come up with a better answer than this.
Your answer to the second part of the prompt also doesn't appear until the very end, and it is this:
I will bring knowledge of diversity that I have learned through my volunteer experiences, an attitude of acceptance, as well as a determination to succeed that will, hopefully, affect others.
This is a bit better, though it would have been nice if you had opened with this then told the volunteer story, but it is still very vague and boilerplate.
So, I'd suggest trying to come up with stronger answers to the prompt questions, putting those answers at the beginning of your essay, then using your anecdote to demonstrate the truth of those answers.