Logically, could the word "University" mean the opposite of "Diversity"?

Solution 1:

Ignoring the fact that the word "university" doesn't mean the opposite of "diversity," your logic has a flaw: The "di-versity" comes from the Latin di(s)vers-, which has the same "dis" as in the Latin synonym divertere, namely "apart." Both words mean "to turn away."

"Dy-," meaning two, comes from Greek. "Twice" in Latin is bis.

Solution 2:

Somehow, the meaning consisting of one does not imply that it is not diverse.

Indeed, the meaning of universe, which is the one that everything is included in, implies that it has everything and thus it entails a huge diversity.