Ironically, I was told  - by a female doctor - to eat red meat precisely because of a female-specific health problem.

Hmmmm...

As for the role meat consumption plays regarding gender, you are right that it is a symbol of masculinity.  I've seen it with my own eyes.  But I think it is a symbolic ritual not meant to express masculine bravado in order to oppress women, but a sad longing for the animal inside them that they have killed in order to become civilized human beings.  I think women experience a lot of things, menstruation, childbirth, that gives us that feeling of still being part of nature, of being wild somehow, of the ... gore.  I think it is harder for men to find a safe way to tap into that part of their psyche.

Those who can make you believe absurdities can make you commit atrocities. -Voltaire