Well, –“He also began his Metaphysics class with the statement: “Metaphyiscs .

Well,
–“He also began his Metaphysics class with the statement: “Metaphyiscs . . . is FALSE.”–

Depends on how he made that statement.
He might have meant that all metaphysical claims that are not physical must be false. In the context of realism and naturalism. i’ve made the same argument. There is only one physics.

We use metaphysics as “presumptions” despite those laws. In that sense, metaphysical presumptions do exist.

The difference is that one is a claim about the universe and the other is a claim about our presumptions of the universe. 😉

😉