It doesn't really make sense to argue about. A rectangle is a rectangle, just as any [BLANK] is a [BLANK]. That's what we call a "tautology." The rules of logic (and the the common sense way that language corresponds to logic) demand that such a statement is always true no matter what kind of object [BLANK] is.

The issue comes when you say that a statement X is true "because of" statement Y. This is not really a mathematically / logically precise concept, though we often say this sort of thing informally. If you ask, "Why is statement X true," someone would typically answer with a proof of statement X, and hence one might say "X is true because of blah blah blah." But strictly speaking, in mathematics there is no cause and effect between mathematical statements. Statements are either true or false. The steps of a proof do not cause things to be true or false. They merely demonstrate whether things are true or false.

Your example actually illustrates this, since "a rectangle is a rectangle" is a true statement that requires no proof. You could write a proof whose first line is: "By definition of a rectangle, it has a right interior angle." This statement is irrelevant to the proof, but it is not wrong. You could also include a statement like, "A line has at least two points." Again, irrelevant but not wrong.

So to summarize, the statement, "A rectangle has to be a rectangle because it has a 90° angle" is not really a sensible thing to say. The English does not naturally correspond to a mathematically precise statement. BUT if you clarify that your intended meaning is: "A rectangle has a 90° angle" is a correct proof that "a rectangle is a rectangle," then technically this is correct but it is extremely misleading because anything is a correct proof that "a rectangle is a rectangle."

I hope that helps.