"Well, it is a private university and does have the right to determine what is and is not acceptable behavior for its students,..."
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If he, say, spray painted anti-homosexual remarks around the school property, then yes. But this is a matter of a young man making comments in a forum not related to the school. Has nothing to do with behavior, but rather, whether or not this man's freedom of speech has been violated.
Sorry, but with a private school it's all a matter of what's covered in the contract between the school and its students.