If one disagrees with an argument because it's superficial, then one might call it "specious." If one disagrees because the argument is invalid, then the word is "spurious." I think based on the counter argument, "spurious" is what was wanted.

https://www.merriam-webster.com/words-at-play/specious-vs-sp...

I think either would be appropriate but I suggested specious because it rhymes with facetious and I often mix up rhyming words myself.