From a woman's point of view, I would say that women world wide don't like being asked their age as then the asker tends to stereotype them, eg oh well what can you expect, she's past it etc.

For some people its very personal especially the old folks, they attend taking it more seriously when it come to age. But if you ask me I will say age is a question of mind over matter. If you don't mind, it doesn't matter.

In the main American culture it is a rude thing to ask unless your lose with that person. In America youth and a young look is revered, not exactly sure why but I'm sure it might have come from 1800s, when wealthy men mostly married young woman. Possibly higher chances to have children.

Because it's a personal question, and you shouldn't strangers personal questions. Also no one wants to seem old!