They want to look down their noses on poor people and make broad assumptions that all poor people are criminals or "less than" they are. They want to feel elite and more special, and not only that, expect special treatment from others as though they actually were above.
There are plenty of gated communities that others can't afford. If they're too good to be among the rabble of us, the middle and working class, let them go elsewhere and live in fear behind their gates and miss out on the real richness of life, which is diversity and knowing more than what is in one's own little corner of the world.
Rich against poor is a form of discrimination, period. Don't want to be around poor people? Fine - move. problem solved. Forcing people who live in the same building to use different entrances etc. is not right. These people aren't royalty because they have more money. Money might make one wealthy, but it doesn't make you rich. If you feel you have to isolate yourself with only those of "your kind", than that's not richness at all.
Thankfully, most of the wealthy people I know in our area do not have that mindset. They are friendly with the rest of us in our area and don't isolate themselves behind gates etc. Our children play together and attend the same schools. Only a few are like the ones you mention live here - and no one, not even the other wealthy people, respect them, not because they have money, but because they are profoundly arrogant.