The government heavily subsidizes every university, both directly (in the form of research grants, student loans, etc.) and also by setting up a favorable tax structure. Governments subsidizing universities results in large social benefits, and should generally be applauded, though the form of those subsidies could use some structural changes.

The home mortgage interest deduction is the same thing, mathematically. Is Harvard also being subsidized by the Feds via rich professors living in Cambridge?

Yes!

OK well, now all government benefits (and roads, and defense, and NIST, …) are “subsidies”, and it’s not clear why taking advantage of one—by Harvard or anyone else—is somehow counter to the reason the government is spending the money in the first place or otherwise worthy of scorn.

Now you've got it. We're a democracy and we tax ourselves to buy things for ourselves.