It's intrusive from a stranger or near-stranger; we're not at the point of getting to know each other and figure out whether we have things in common and might become friends.
I will cheerfully tell people how old I am--but that's as much because I think a woman shouldn't be judged based on her age and appearance, as that I believe I won't be. And it's illegal to ask "how old are you?" in a job interview, but once you're hired, at least in the U.S., the company knows that. Your manager might or might not, but HR does: when I was laid off a couple of years ago, I was given a list of employee titles (not names), ages, and whether the person had been part of that layoff, in case I wanted to argue that I had been the victim of age discrimination (in other words, so they could convince me not to waste my and their time and money with a lawyer on that).
There's all sorts of information that I may volunteer, but that is rude for someone to ask, or rude to ask a mere acquaintance. Sometimes it just feels personal, and sometimes it's things that people may judge you for. (There are, unfortunately, a huge number of things that people will be judged for that they probably shouldn't be, including some health issues as well as age and appearance.)