Normal to be offended when someone tells you you are typical (wo)men?

"Typical Woman" and "such a girl" are usually meant to be at least somewhat offensive - and are usually said because you tend towards being "whiney and complaining princess".

So, the solution is simple - stop whining and complaining!

Alternately, own your inner bitchy princess, and tell the world to go take a long walk off a short pier. You should be true to yourself (even if that truth is that you are a whiney complaining princess).