I agree.The World Health Organization's defines gender as "socially constructed", and sex as characteristics that are "biologically determined", drawing a distinction between the sex categories of male and female, and the genders "girls and boys who grow into men and women".
journals.physiology.org
While sex is sometimes non-binary, and/or ambiguous, gender can be fluid.
Because gender can be fluid, and because 'man' and 'woman' are genders, a man can be a woman, and vice versa.Your claim that a man is a woman is erroneous.
But Male is not Female. But sex can be non-binary and/or ambiguous.