Ah, yes. I remember this. Wacko, right?
For what it's worth, I was accepted at Berkeley, so my approach was probably not totally off-base (not a deal-breaker, anyway). Here's what I did.
I gained the most clarity about the genre by defining the OTHER essay required (Academic statement of purpose or something? I forget what it's called): this one was a pretty straight construction of the problems I'd like to tackle with my PhD work and my past research, along with fit, etc. So pretty "just professional," if that makes sense.
For the personal essay, think of it as YOUR LIFE = GOTTA GO TO GRAD SCHOOL FOR X. That is, what will make you tick as a grad student? What about you and your history compels you to do X? In short, why are you going to grad school? What do you think needs to be addressed in the academy, and why?
As a gentle chiding: maybe you haven't been discriminated against as a white, middle-class, hetero, able-bodied male, but you inhabit that position somehow, right? Diversity (or "lack thereof") doesn't have to be experienced as despair or as guilt. And I don't think that this particular essay is a "diversity" essay per se-- more a life experience one.