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This will work. Public interest law, however, is much broader than your narrowly refined definition. Your personal statement may raise concerns as to whether or not you are in therapy--which should be viewed as a positive--or, if not, why not ?

i agree with the commenter above that your definition of public interest is quite narrow. Maybe "for me, public interest is about..."
also, sorry to nitpick but i would say CUNY Law School prides itself in etc and put that whole sentence in singular.

thanks. i revised it a little bit. hope its a little better.