TobyJones I agree with you but I would go further.
Mentally they are really no different
Boy brains and girl brains differentiate in the womb under the influence of testosterone. Even before they are old enough to be socialised baby boys and girls reliably demonstrate differences in interests and aptitudes. In his book We are our Brains the neuroscientist Dick Swaab describes numerous differences in the architecture of male and female brains.
When babies are born who with intersex genitalia it used to be believed that doctors could decide the sex and parents raise them accordingly. In 50% of cases this is a disaster for the child. Best practice now observes the child until it can be determined how the brain was sexed and then perform surgery on the genitals.
What I am NOT saying is that men or women are more intelligent. We are also talking about averages measured over a group which is why individual anecdotes are not useful.