It ends up being used to dismiss women levying legitimate criticism. It basically gets used to enforce patriarchy. In practice the opposite is not really true of “bellowing” to the same extent. But even then, gendered insults are falling out of favor in general.
I am under the impression that, on average, men's voices are lower than women's voices. Hence some connotation.
Doesn't mean men cannot screech, though. Just that there is some reason for making that connection, so at least some folks will make that connection.