I like (as in I find interesting) the "false dichotomy" fallacy. This is where a person is only faced with two options to choose from, therefore forced to go down one of two lanes, which may both be incorrect. In reality, more than these two options exist, but because that's all that is presented to the argue-ee, it's easy for them to lose sight of other options or get backed into a corner by the argue-er when they choose either of these "wrong" options.

I have seen this happen with hiring managers (only 2 people had applied for a job, neither of them were the right fit, but the manager felt pressured to choose one - when she could/should have opted to wait and see if a better candidate came along) and also with arguments about sexism (a man asked me "which would I prefer - a guy who called me and presented me with plans for a date, or a man who called me and asked me what I wanted to do/had no plans." When I said "Well if he had plans I'd love to hear them, but if I had something I wanted to do I would also propose that" he said "Well why didn't YOU call him up if you had something you wanted to do?" and I was like "Yo dude, you presented me with an either/or situation, I realize there are other options, but you can't yell at me for not taking an action in a scenario where that action was not presented." - which I guess is kind of a variant.)