Maybe sockpuppetry is at work?

Who has (read) access to the "who up-/downvoted what?" portion of the database? This might well be something easy to verify, and if so it may be something for a mod to squash.

whoever did downvote proves that they either have a vindictive sense of humor or else that they believe groupthink is legitimate.

A downvote technically means "I want to see fewer comments like this". Someone could easily dislike the parent without either of those propositions being true. For example, one might downvote for the use of "LOL".

I don't understand how you would think that it's impossible for you to be downvoted at the same time as your opponent is upvoted.

I don't think that's what wedrifid said. Rather,

me getting downvoted I can understand

explicitly acknowledged that being downvoted isn't terribly surprising when being frustrated and fussing over what was said.

But xxd has been upvoted here. This makes no sense!

was expressing exasperation at the fact that you would be upvoted when you seem so clearly to be responding to something never said, regardless of whether his comments went up or down.

My downvote on parent was because it missed the point so thoroughly - I don't know about the one that preceded it.

Personally, I downvote all comments which contain statements impugning the motives of downvoters, regardless of other content.

It has the pleasant side-effect of rendering most such statements false.