Separating children and teenagers into 'boys and girls' keeps reinforcing the idea that these are part of some black and white, unchanging reality.
The fact of the matter is that both the gender and sex binaries are a complete lie. From fluent gender roles to a wide variety of physical characteristics (where'd an intersex/hermaphrodite person like yours truly fit into this system, for example?), making a school 'girls-only' or 'boys-only' merely opens the can of worms of 'what's a girl/boy?'.
Is a transsexual boy or girl a girl or a boy? What about someone who is 'genderqueer'? What about an intersex person (pick one of many dozens of conditions there)?
For these reasons 'gender-segregated' schools feel more like an artifact of an ancient, ignorant society than something which we should admire or strive to imitate.