There's one kind of argument I particularly hate to have

...and that's rationalizing. Typically, it occurs when the person I'm arguing with has a gut feeling about what's Right, but can't maintain a logical defense of the position. I can chip away each path of apparent logic they use in defense of a position, one at a time, and then they'll come up with some new path, or switch back to an old path with a different tact.

What's frustrating about it is that it tells me there isn't a logical basis behind the defense of their position, but an emotional one, and logic is simply the mechanism being used to defend it. That means that they're exceedingly unlikely to ever change positions, unless and until that emotional basis is identified and resolved. That's pretty difficult to do when the person holding the position can't acknowledge the basis behind their core position.

The particular argument inspiring this rant was my expressed frustrations that AdBlock Plus is overly aggressive, and blocks the queries that build Amazon referral links--I was going to use those links in-line in on-wiki citations and user-recommended resource links. With ABP running, one gets a big, fat, red "Unable to retrieve data" blob of text. I'll have to mod the MW extension to deal with the error case.
I can understand wanting to block distracting and attention-grabbing advertising content. Blocking referral-building and search AJAX queries strikes me as going rather far, and smells of anti-commercialization intent rather than simply consumer protection.