So I'm not sure why fans of a team across the Atlantic would route against us? Particularly given the team you do support wouldn't exist in its current format without us.
I will add that this particular part of your post, in the early days of this forum, got spouted an awful lot of times by MCFC fans (and I say this as a British City fan myself, so this is not biased ranting...) and caused a huge amount of friction, not to mention a lot of site bans. As the others have said, simply put the older members of this forum are sick of this subject so I won't give the long reply I once might have, but to put it simply MLS was looking for a long time for a way to introduce a proper NYC team (the Red Bulls don't count) and Barca and PSG both could have bought the club while it was equally likely that an independent investor could've bought the franchise. To suggest that the club literally only exists by the will of MCFC is a bit facile, and not very accurate. If anything, the idea that NYCFC fans should feel gratitude to MCFC fans for their club's involvement is considered fairly insulting.
When Barcelona expressed interest in owning an MLS team, possibly in New York, possibly in Miami, they were put off by the MLS single-entity structure. They wanted to operate in the traditional manner: they wanted to be able to transfer players at will from their main club, and to have unilateral control over player acquisition. But there was no way that that could happen within MLS's model. Similarly, the thing that dissuaded the Cosmos' owners from buying the New York club was the MLS business model. For the Cosmos, paying $100 million only to lose all rights to their name was not a step that they were willing to take.
Manchester City's ownership was the first group from a big club that was prepared to deal with MLS as it is. CFG agreed to become an investor-operator within MLS's structure. For them it was enough to establish a new team that had a name and a general look that evoked their flagship team in Manchester, without demanding any special privileges over existing MLS teams.
I have never been a Man City fan. I am a Chelsea fan; though I have great respect for Man City. (We share a hatred for United.) The previous City ownership under Thaksin Shinawatra brought that club out of the shadows; and the Mansour group has begun the process of entrenching City amongst the world's biggest clubs.
As a Chelsea fan, I am 100% in favour of having rich owners who stop at nothing to build a great club. Also, fans of all other teams owe a debt of gratitude to clubs like Chelsea and City; great owners such as the ones at these clubs raise the bar for the entire league, forcing other clubs to spend in order to keep pace, or else to sell to better owners. The result in England has been the redemption of football, with the purging of the violent element from the stadiums, and the continued influx of ever-growing television money that has allowed even unglamourous clubs to bring in high-quality players and not just be content to be selling clubs.
So Man City are on the right side of history; and I am very pleased to have my team associated with this. Those who dislike NYCFC try to use the connection with Man City as some kind of insult, calling us "Man City lite" or "Man City's farm team" (notwithstanding the fact that there can be no farm team in MLS, as Barcelona found out to their chagrin). I find that the best way to shut this kind of critique down is to completely own it. When people attempt to put down NYCFC as "Man City lite", my response is: "Yes, indeed; and damn proud of it."