Do we actually know why sane wants out ?
Does he just he wants to go home or is he not happy at city ?
Iv never thought pep liked his attitude to be honest, he’s never been the first name on the sheet.
There seem to be a few things. In no particular order: (I've probably missed something)
1) It's Bayern. If you're a German lad this is reasonably as good as it gets.
2) Also it's Germany. It might just make him happiest to be in his home country.
3) Not getting selected for the 2018 World Cup has made him feel like he needs to be somewhere he'll get more game time. If it's in Germany then even better.
4) Apparently there's more money on offer there.
5) His family have apparently pushed hard for this. Particularly his mother.
6) The lack of game time in general. He always got games but he might believe a player of his qualities should be featuring as often as Sterling. He'd get that at Bayern.
7) Unwillingness to work harder. Sané has consistently had the label of a questionable attitude. Even back home in Germany. Compared to Sterling, Bernardo, and Jesus, his lack of defensive work rate is apparent. Even players like Gundogan and Mendy who get criticised (rightly or wrongly) for their lack of defensive abilities can't be accused of being lazy.
8) We'll never know this for a while, but it's possible that his relationship with Guardiola broke down to some extent. Enough to make him turn his head elsewhere.
Although to answer your question directly, it's probably more to do with wanting to go to Bayern than to leave Man City. There's never really been any major stories that Sané is unhappy in Manchester or at City. But the fact he'd always been hesitant to sign a contract meant that either he felt his future lied elsewhere or he knew Bayern had been after him for a while.
This Sané thing makes you appreciate guys like Foden, Jesus, Danilo, and others, who at several times have or had been advised by the public to leave the club in search of greener pastures but were willing to stay and fight and not ruffle any feathers in the process.