I don’t have the time or inclination to discuss all the ways I think you are mistaken, but a quick synopsis might suffice.
He definitely has the option to hold out, as does every player, which begs the question why every player does not just run down their contract, take a big pay check from the next mug club to come along and mint it?
If he wants to play in England (which is the only league in the world where his lack of technical ability allows at this level), and wants to make £10M+ per year, just from playing and before endorsements, and play for a team where the manager picked him up off the floor and is helping turn him into a player, and where he will win trophies every year or so while challenging for the very best trophies in the world, then he will sign. If not, good luck to him...he will need it!
He has a very special situation at City. He should recognize it.