[someone edited] my answer [to] change their upvote to a downvote. Is this a valid tactic?
As mentioned by other answerers, this is the only way to do it. It is valid and permissible.
It seems incredibly disrespectful and rude.
It seems that way because it implies that they have modified your answer to disagree with it. This is a red-herring, they were doing what they had to do in order to downvote an answer they felt was wrong.
It is important to sometimes remember that not only are downvotes very minor in the scheme of things but that they are meant to indicate one user's opinion about the correctness of your post. Downvotes are not about disrespect, they are about accuracy.
This has seriously pissed me off. I've been answering this person's questions over the course of the past 12 hours,
Anytime you are angered by something, the best response is just to walk away. It's -2. Your rep is quite healthy, so the -2 will not affect you. Getting angrier will not lead either party to any revelations, you'll just come to hate each other more.
and further more he's completely wrong about his reasoning.
See the last line of the previous paragraph. But, assuming that you are correct, and he is wrong, and you are willing to stay and politely try to convince him, then you should be aware that there are stubborn people who won't necessarily change their mind without something drastic going on. For instance, if you were to create code to test both methods and post it somewhere he can access. That would prove your point, and you could do it politely.