Same sex schools should not be put into place anywhere. I feel as though it is wrongs to segregate from the different sexes, especially since there are many different definitions of gender. Someone who was physically a boy, would maybe have to go to a boys's school. But what if they're a girl mentally? They would end up not belonging in any group, as they would have different view and thoughts as everyone else, and might not fit with the status quo. Gender fluids would have a hard time with this too. Part of the time they'd be in the right school for their mind and body, and part of the time they'd not only be in the wrong body, which is difficult as is, but they'd be in the wrong school. Both of these situations are basically begging for bullying, and making people feel uncomfortable.
I went to a very prestigious boys' school in the UK (albeit with a girls school as well), I won't tell you exactly where because well - Internet security. I was no obliged to go there, I passed exams for two other schools, one of them with people of both genders. The point is there are some advantages, and the girls' school next store took away many of the disadvantages. I would completely understand if we are in a situation where there are no mixed schools, but there are plenty. Same gender schools are not obligatory, and almost all schools who that a very good reputation now but don't have much history tend to be mixed anyway (e.g. Latymer Grammar School). Even the most prestigious and historic schools like Eton take both genders in the 6th form. In primary school from receptions to year 6 the only same gender schools are prep schools anyway.
I've just realised I need to stop using 'anyway' - anyway,
R1: My opponents arguments seemed desperate, yet any education system in a desperate situation would not have same sex schools, as they are inefficient, but in a privileged society like ours, we can afford to have a wide range of schools. If they want to be in a mixed school, they can, but if they are bored of the conflicting attitude of the opposite gender they have no obligation to be at a mixed school. It helps a society in which education is more or less hated, and that is not it's purpose.
R2: Same sex schools give a higher chance of finding someone similar to you, especially in terms of ethnic mix, that in the UK at least, is enormous.