Mustache

I prefer not that a woman should grow a mustache and beard to prove she is a man

Does a man need to prove he is a woman?

No.
One doesn’t need to be a coconut, nor an oreo cookie, nor an uncle tom, nor an autie tammy, nor a house negro, nor a house arab, nor a south asian who looks like a cartoon when mimicking the (pretend) images of western folks in TV advertisements.

I subscribe to the notion of Ying and Yang

Both feminine (women) and masculine (men) are required for balance