It argues of “impossibilities” and also proves it.

I think you need to read it again.

Gödel wrote his teorem to test David Hilbert’s endeavor, Logic and the Foundation of Mathematics[0], to unify mathematics. Gödel proved that it is impossible to do.

But you may have a different version of history.

[0] https://www.famousscientists.org/david-hilbert/