Alexis is not signing for a club he doesn't want to play at, simple as that. On the other hand I also think he would have wanted to play for City so I don't think he rejected them for us or anything as dramatic as that. Before United entered the picture it was reported City had an agreement with Alexis but not yet with Arsenal.
I don't find it hard to believe that City might not want to make Alexis their highest earning player in the squad and I also don't find it hard to believe that they maybay view as more of a luxury signing that they aren't willing to go the extra mile for unlike United. Their loss, our gain. I also think the fact that United could include Mkhitaryan in the deal helped a great deal with getting this done because don't forget Arsenal will not sell to City if United offers a better deal and it seems like Sanchez prefers to make a move right now rather than wait for another 6 months.
Conclusion is that City really isn't some magical club that star footballers would want to join over any other team even if it means less money. To be clear United isn't either. But seems like City has been acting a bit like one in this transfer saga and it will cost them the Sanchez deal but given how good their team is right now and that are walking the league than maybay they don't care. I actually have a massive deja vu feeling of back when Fergie was walking the league and was close to signing Hazard and than last minute it got hijacked by Chelsea because we didn't want to further increase our offer. It kinda feels like that a bit but it seems this time we are on the side that gets the player instead of keeping it is unexsiting principles in tact.