Single-sex education was around long before scientists were debating whether male and female brains differ in important ways. Some parents support single-sex education, especially for adolescents, because they think the presence of the opposite sex can be a distraction in the classroom. Others envision different roles for their boys and girls as adults, which leads them to educate them differently. I'm not saying those parents are right or wrong or that single-sex education is good or bad, just that it is as much a question about values as science.
Another reason is that being educated in a single-sex environment can, arguably, go some way to counter stereotypes prevalent in your society about what girls and boys "ought" to be interested in or good at. For example, it's often said that it's socially easier for a girl to be good at STEM subjects in an all-girls school than it is in a mixed school. In a single-sex school someone going against stereotype is being taught in a class with others who are also doing so (inherently challenging the stereotype), whereas in a mixed school, s/he may have to do so in a class which is mostly populated by the opposite sex and may find the stereotype reinforced rather than challenged. Some children find this no problem at all, others do find it an additional hurdle. Not saying this means single-sex education is good overall, but it's a consideration.
It's a lot more comfortable to schools, though, to be able to appeal to brain science to justify being single sex than to have to discuss touchy subjects like stereotypes and children being distracted by the presence of the opposite sex! Which is probably why they do it, and they'll probably carry on doing it...
