I really could give a hoot if someone wanted to know how old I was. It doesn't offend me in the least. Age is just a number.
Of itself? No! But some people are tetchy about revealing their age and may be offended. And, since it's rude to offend, it may sometimes be rude to ask a person's age. It's a matter of judgement.
I'm 25.
Definitely Three Men and a Baby