Here's an excerpt that pretty much nails it:
So what occasions the essay? If a writer has no surefire argument to make, no point to sway the reader toward, why flaunt personal vacillations in print? Why not leave the questions and doubts to the rough draft rather than give them life?
For Richard Rodriguez, the attraction is the essay's public rehearsal of ideas. . . . "For me, the drama of the essay is the way the public life intersects with my personal and private life."