One of my favourite quotes is that 'communication is an act which takes place between equals.' That is, two people, on equal footing, with a mutual understanding that both sides of the discussion will ideally be fruitful and in good faith. In Discordianism and anarchist philosophy, that's known as the SNAFU principle, because two individuals on a corporate or hierarchial ladder are rarely so equal and so can never have a completely honest discussion.
Trying to convince a zealot fails all three tests consistently. It's not on mutually equal footing -- they consider themselves inherently superior in all ways. It's not in good faith -- they will say anything to get you to give up or agree. And with those two points, it's evident that the zealot lastly does not consider the interlocutor to be a person, but a game to be won, and ignoring the question is just one way to do that.