This topic though to argue with your mother about is particularly galling.
I'd say look. I am a woman. You are not. I have been around much longer than you and have seen heard and experienced plenty in that time.
As a grown woman I am telling you that-
Putting male criminals convicted of violence/ sex offences against women in women's prisons is obviously a massive risk for the women. And they can't get away.
Having males go into any and all areas that are set aside for females, based on an invisible feeling in their head. Areas that have always been separated by sex for good reason. Is obviously asking for trouble. Due to the very large number of creeps about.
Etc etc.
If that's not going to work/ you've been through that.
Then ask him to be honest as to whether all the boys in his class would have been totally comfortable getting changed for swimming/ PE. With a fellow student they have known as a girl for 4 years. Not embarrassed? How would it feel for a boy who had a crush on them for ages? Wouldn't it be really just bizarre to have a classmate in there with a developed female body?
Ask him if he knows how women are treated under the taleban and how do they know who to treat as a woman/ girl. Just ask him. Because it's got nothing to do with how anyone feels inside.
Tell him that women and girls experience loads of words/ actions/ assaults from horrible and or creepy men. Say this is why single sex things exist. Say you're going to turn it around. Ask him how he can guarantee that gender > sex will have no impact on the comfort/ safety of women and girls when they are in situations where they are undressed etc.
And if he still says nope.
Just say. We disagree. I am not interested in trying to explain the differences in male and female, or why women and girls are vulnerable to dodgy men.
There is no point in us talking about this any more. We'll have to agree to disagree and keep off the topic.