I can't agree with this more. I live in NYC and it is a very different pace & way of life than anywhere else I've ever been. You can't stop to hold the door for everyone, you'd be standing there all day! I do hate blatant rudeness though, and when my DD is old enough I will teach her to be polite. I will stop to hold the door open for someone who needs help (pushing a stroller, carrying bags, elderly, disabled, etc.). Also give up my seat on the subway or bus to someone eldery, disabled, or pregnant. It really burns me when I see a pregnant woman get on the train and not one man gets up to give her a seat. A lot of people just pretend they don't see her, and more often than not its a woman who ends up getting up for her. Another thing I hate here is when someone runs right into you on the sidewalk and doesn't even say "sorry" or "excuse me." It's a crowded place so these things happen but at least acknowledge that you just rammed into me!
Funny story, a couple weeks ago I was leaving work and when I exited the building I accidentally ran into a woman who was walking past on the sidewalk. We both turned to each other and said sorry/excuse me at the same time. Then she laughed and said, "I think we're the only civilized people left in this city!" (This probably makes NYC sound like a horrible place, but its not. Despite any rude people I encounter I still love it here.)
I think the tourists might have something to do with it. I get really aggravated with the tourists here sometimes. Like families who walk 4 or 5 abreast, blocking the whole sidewalk. Or large groups who stop dead in their tracks in the middle of the sidewalk to consult a map or take pictures. Move off to the side if you need to stop! I avoid the touristy areas whenever possible, but if I have to go through them I probably seem somewhat rude. Just know that I'm not trying to be rude, I am just trying to get somewhere. NYers walk faster than anyone else too, so to us you all move WAY TOO SLOW.

Let's make a deal, you promise not to stop dead in the middle of the sidewalk and I promise not to give you the wrong directions to the Empire State Building.