I sympathize with the argument that cutting the genders in two can deny student's an opportunity to socialize with the opposite gender..........At school. If we used this as the only reason not to look at gender specific schools, it would be illogical, as schools are not designed to teach socialization but math, science, etc.
A student is still capable of socializing with students of the opposite gender outside of school. While children are still gender neutral, before puberty, in a co-ed school, they socialize with the opposite gender. And a large majority of children have both a mother and father, as well as female and male relatives and possibly a different-sex sibling. To assume a student would never have enough contact with the opposite sex throughout life to socialize to them describes and extraordinarily unique situation that should not be applied to the majority.
I believe it can be an advantage to not deal with the opposite sex at school. Take an average teenage girl after a breakup for example. Having been one of those myself, knowing I would have to face my ex boyfriend at school was horrifying to think about; because we were co-ed, we shared many friends who would now take sides. I'm sure this happens outside of school to, but we're talking about in school, and in school this is distracting. It places a non-scholastic drama in the realm of the scholastic, and it does have an effect on achievement. You might also say that bullying has the same effect. But studies actually show that bullying between girls decreased significantly when boys were taken out of the equation. (sources in comments). Further, girls are actually more likely to be bullied by boys (75% by boys, 25% by other girls) in co-ed facilities, so the gender separation has a twofold benefit.
There is, finally, the point of schools reinforcing stereotypical gender roles in often harsh and unfair ways. I do believe this is a co-ed problem. As it turns out, girls are more likely to be ostracized for not fitting into traditional roles by OTHER STUDENTS. After the 1970's shift toward working women, the education system took steps with teachers to thwart their support of stereotypical gender roles. They take classes on how not to do this very thing with their female AND male students. But this has opened our eyes to the greater problem, which is their peers. A girl is significantly more likely to end up in a gender traditional set of high school electives because her other female friends do. Girls in female only schools may not fall into this same trap as they are accustomed to many females taking many diverse classes. They are also unlikely to ever hear a teacher say that boys are naturally better at math, or worse to SEE a math teacher favoring male students.
Having grown up in a country where the national educational system urges regular schools to make attempts to separate their students based on gender (until, ultimately, they study and learn on two independent campuses), I can tell you I felt unhappy attending school essentially cut off from female interaction. Students in gender segregated learning environments (where interaction with the opposite sex is often frowned upon and near prohibited) will spend the bulk of their time with friends of the same gender and will have difficulty communicating or socializing with people of the opposite sex when they actually have to (many may not consider this a valid reason, but it is a very real one, trust me). Many will also feel as though they are "missing out" on something as their daily routine consists almost purely of just one "type" of human. Many will develop insecurities and anxiety related to or caused in part by this.
And although this lack of diversity is unnatural and unhealthy from a social and psychological perspective, an even more compelling reason as to why a system like this is flawed is that the male and female mind are different and often function differently (this has been observed and studied abundantly within the last half-century). The approach taken to a problem by the average male may be drastically unlike that of the average female. It is for this reason that I believe a non-segregated learning environment provides better ground for students to share ideas and carry out discussion.
Another thing to point out is that, particularly in classes existing in the middle school-early high school transition (grades 6 to 9, possibly 10), male students are often at an age where they may not always act mature and are capable and willing to cause serious disruption to classroom activity. They are also at an age where they really CARE about their reputation and are conscious how their peers perceive them. In a class consisting purely of other boys, these two factors combine and the individual may feel inclined to disruptive behavior and/or rebellion to assert dominance, a disregard or superiority over school, and similar unhealthy visions of themselves. In a class that's mixed, however, the student may refrain from causing serious trouble out of fear that the girls (who are usually calm and better tempered) might deem his behavior distasteful. A lot of people would disagree and say that the presence of females may actually encourage them to act obnoxiously (as to get attention) but this is usually not the case when dealing with teenage adolescents. The majority of 13-16 year old guys refrain from clowning around in the presence of girls their age.
In principle, standard, non-segregated schools typically cultivate students that are more socially functional, students that exhibit better behavior on average, and students that experience more beneficial and diverse academic interaction with their peers.
*My opinion and this question are under the assumption that standard and gender-segregated school are IDENTICAL in all other aspects.
This question has come up a few times. Single-sex schools do tend to have higher grades, higher graduation rates, and lower truancy issues with students tending to be better within the school community and environment.
In principle, that is ideally, if all were the same, then no. So really in a hypothetical perfect universe it works, but in a realistic one it does not for so many reasons. One of which is that the opposite of all you've said is true; boys tend to show off more, not less, in the presence of women, or rather I should say "males" as that never fades, and secondly there's no evidence that a person is more or less socially functional or behaviorally more appropriate between the two school systems. That's very utopian.