There's a lovely term now called pigeon chess, which describes the frustrating experience of trying to debate someone who refuses to engage you in a sane or rational way, instead filling the dialogue up with logical fallacies and obfuscations, and often declaring themselves the winner of the "debate" thereafter.
The term was originally coined by Scott D. Weitzenhoffer, who in a 2005 Amazon book review comment titled "Problem with debating creationists," remarked:
Debating creationists on the topic of evolution is rather like trying to play chess with a pigeon -- it knocks the pieces over, craps on the board, and flies back to its flock to claim victory.
I recently wrote an article about Jill Stein, the headline of which contained the word "mansplaining." I wrote that I liked that word because it finally provided a word for that weird, creepy thing men do when they assume authority over you when they have none.