The smartest thing I read about the question "What does it mean to be a good man?" was that the question was wrong - it should simply be "What does it mean to be a good human being?" In my opinion, it's a much easier question to answer.
Whatever your circumstances, whether you're a man, woman, something else; some of that is a given. It's not just who you are or who you chose to be, but the expectations and opportunities made available to us based on who we appear to be.
It is a relevant question to ask what is the best way of playing the hand you were dealt by circumstance.
I think it’s because “a good man” is quantified by the indefinite article “a”. Whereas “man” in a sentence without that qualification, e.g. “one small step for man” I would not interpret the same way. So, “a man” = a male human, “man” = maybe a male human, maybe any human.
Some problems are specific to men or women exactly because our society has different expectations for men and women, so general advice good for one gender is not always good for the other. Example:
Q: How to be more appealing to the other sex?
A: Wear some light makeup and a nice dress.