Honestly I think Arsenal just weren't interested in him anymore (also has been a tweet saying they told Barca, they wouldn't activate the buy-back clause they had on him), I can also see why, they simply don't need him anymore, last year when they didn't have Ozil it would have made sense for them to sign him when he would have become available, but now it would be pointless for them to sign him, they don't need that type of player. The only reason for them to sign him, would have been for emotional reasons, and that is never a good basis to spend £30m on. They have Ramsey and Wilshere as deeplying playmakers and both are more than good enough, futher up the field they have Ozil and Cazorla, they simply don't need him and a club like Arsenal will never spend that kind of money on a player they don't really need (especially with so many other positions, they need to strenghten in). It is like us being linked with Cavani or Falcao, they are good players, but we simply don't need them atm and hence why it doens't make sense to spend a ton on signing them.
As for the fact that Fabregas chose Chelsea, I think more than anything it has to do with him wanting to play and live in London. He has lived there for many years, it would be like coming home for him. That probably swung his decision towards Chelsea instead of us or City.
Manchester not being an option cause it ain't London and Arsenal not being an option because they don't need him and won't spend £30M on him, that makes Chelsea the only other option.