LadyFanny we've had a few threads about the term "a man's woman" but Madam is right that it's a particular red flag if that label is self-awarded and worn with pride. There is some confusion too about the term, because it seems it's often applied to un self-conscious women who can't relate to frivolity and "girlyism" and prefer the perceived directness and honesty of male company.
However, the term often applies to women who actually dislike other women and see them as competitors. Such a woman can often be found running other women down for their appearance, their feminism, their assertiveness, their right to a career and most of all, their inability to "keep a man happy".
Hence, in the company of men, this woman will simper that she is not one of those hairy feminists who will give him a hard time if he watches porn, wants sex on tap or any other "need" that she attributes to men as their "right".
However, once in a relationship with her, she is a mass of insecurities and exhausts herself trying to be the perfect "man's woman" and in fact gets hysterically jealous if he does anything that implies she is not catering to his every need. Cue major drama and sulks, because all of her self-esteem is built on her appeal to men and any sign that a man might just need other stimuli such as friends, a hobby or some time away from her, is perceived as a threat.