As a native, this is the crux of the issue. Traffic enforcement in NYC (specifically, Manhattan) is atrocious. So many cars run red lights, make illegal turns, block the sidewalk, stand illegally, etc. It's self-perpetuating, the more people see others get away with these infractions, the more likely they are to do it themselves.
They really have to start fining people for every single infraction, especially the minor ones, to change the horrible car culture in the city.