The problem here is that you grant Michael and Franklin their 'manhood' without questioning it, but then where is the 'womanhood' which should be granted to any female characters?
The whole idea of 'manhood' being a thing which men should have by default, which GTA 'takes shots at', is another structurally sexist concept. I'm not saying you're a sexist - it's a structural thing, ie something which everyone doesn't even think twice about.
But it's not equally bad. It's worse for women. There's so much evidence in this thread of that. Even just a thumbnail analysis of one aspect of character in fiction:
Some male characters have lots of power. Some have none.
Some male characters are always lackeys, under a boss. Some have true agency.
No female characters have any 'power'.
No female characters have any agency. Arguably Michael's wife does, but she's still slave to sexual relationships with other people and comes 'crawling back' when they don't work out.
People are doing the traditional structurally sexist thing here and focusing on the men. "But the men are flawed, too!" Forget that. Look only at the female characters, and look at them in a near-vacuum (only including nebulous/structural connections to male charaters).
Only two women have a modicum of agency/power: the FIB woman, but even she's in love with her boss who isn't interested in her and is insulted by Franklin about this.
And Franklin's ex-girlfriend. She is actually a really excellent character, come to think of it. Probably the only good female character in the game. She doesn't put up with his shit, makes her own choices, and never compromises her principles. She never gets back with him a very logical and well though-out development. Kudos to Rockstar for getting one bloody thing right.
It's a well-known fact that women partake in sexist (misogynist) culture just as much as men. That's because these issues are structural people struggle to see or understand them because they are subtle and obscure patterns throughout society. These are abstract ideas - for example men and women will say 'slut' because it's "what you say". They won't understand that the word was only invented to perpetuate a negative narrative around women.
Thank you!