There is a rather nasty term for what he's doing to you, that actually came from my FWH.
It's call grin-fucking. That's when you smile, agree, say whatever it takes to end the discussion/request, and think F-You mentally. You have no intention of complying with the request and no interest in getting into a discussion/argument about it, so you just make positive noises and do whatever you want.
I wonder. Is he really OK with being labeled a liar?