Trying to get onboard without letting others alight first is just the way things are.
Go to Norway for instance and people don't know how to stand in line. They instantly form a half-circle crowd and instead of an orderly line you get complete chaos. It's just how things are over there.
I was in Barcelona recently and that's where I was truly shocked. Now their subway system might not look the nicest but it's very efficient and the times between trains are a fraction of what they are in Singapore.
One time we saw a lady get off with her little son and walk towards the escalator. And instead of finding the nearest toilet she simply took him aside, pulled down his pants, and let the kiddo take a leak right there next to the escalator as if this was normal procedure. They were apparently immigrants from South America, but still...