I have not used a false equivalence.
I have not claimed that sex and race are equivalent. I am simply asking you; If you think you can explain why it’s OK to segregate on sex grounds, but not on race grounds, please feel free to try to do so.
And I don’t know what makes you think I have a teenage daughter, but my (non-teenage) daughter cannot possibly be incarcerated in an all-male prison — because any prison she went to would no longer be an all-male prison. And I do not object to the existence of mixed-sex prisons. Prisoners should be adequately protected from attack by any other prisoner, whether they are in an all-male prison, all-female prison or a mixed prison.