The answer to how the original person makes this leap is found in the "white flight" debate of the 1960s to 1980s. It's a point of reference that a lot of people on HN don't have (I do not, in any way, want to sound like I'm being demeaning or patronizing; it is an item for discussion, nothing more, and certainly not as an insult).
Having experienced it, and coming from a family that did, basically, just that, the "f-ck you I've got mine" is what drove a lot of that behavior. It could be more accurately expressed as "f-ck you guys, I'm out of here because I have the social, financial, and legal methods to do so," since a lot of the "good" neighborhoods had redlining practices that predated the mass exodus and, even though they became illegal, were still quietly, subtly enforced by real estate agents, mortgage brokers, and nearby property owners. A major symbol of white flight is the rise of the gated community. They gave a way to erect a literal barricade against the undesirables, regardless of skin color but always against "shady" characters.
The last problem is that white flight, and subsequent "I have money"-flight (again, regardless of skin color), essentially drained the urban cities like Detroit, Dallas, Pittsburgh, Atlanta, and Chicago. Some of these are bouncing back--like Dallas--and some not so much. Areas we think of as "Chicago" are, in fact, separate legal municipalities propped up by the massive influx of wealth. The people who lived there commuted into the urban cores, generally on highways paid for on the backs of the people left in the urban areas, to jobs that contribute little to the city where they are located, and then fled back to their quiet suburb where they could enjoy "having theirs."
Is there anything, individually, wrong with what they did? Absolutely not. Those who "fled" took the opportunities available to do them and did so out of an interest of self-worth. The whole point behind flinging "f-ck you, I got mine" as a derogatory remark is that it is half taking out frustrations on a societal dysfunction, half human nature.