In light of Godel's revelation that math may contain a contradiction, proofs by contradiction are particularly disfavored. One can never know logically whether the proof simply stumbled into an underlying contradiction in the math, rather than proving the proposition
... and as commenter "AdrianDelmar" points out, Schafly has completely misunderstood Godel's theorem:
If you are referring to Gödel's incompleteness theorems, his revelation was not really that math may contain contradictions but that a formal system cannot be both consistent and complete, meaning essentially that a consistent formal system will contain statements that it cannot prove true or false within its own system.
I'd hate to see Mr. Schafly try to teach a course on computational theory - which clearly doesn't align with his conservative ideology.