I really enjoy poor arguments that are along the lines of your example. I think it's funny (I mean literally funny, like a joke) to come up with an argument that is almost right except for some single glaring flaw, and present it seriously; can you spot the flaw? I come up with such things on purpose frequently in casual conversation with friends, if I can think fast enough. I don't think we would get along very well!

I also enjoy debugging software a lot more than most people, which I think is conceptually similar; you have a big mental model that yourself or someone else has constructed, but it doesn't work as implemented, because there's a trick somewhere. Where's the trick?