Co-education generates more heat than almost any other issue - among schools, that is.
Single-sex schools can find co-eds infuriatingly smug when they talk airily about being closer to "real life"; meanwhile, the co-eds can get wound up by claims from single-sex supporters who insist that adolescents always end up more interested in each other than in learning.
Similar arguments are repeated endlessly. Girls get a raw deal if they are forced to learn alongside noisy, attention-hogging boys, the single-sex supporters argue.
The gender pressures deter girls from learning physics and maths, and the boys lose out too since they are too busy showing off to the girls. In turn, the co-eds stress the importance of preparing boys and girls to work together in the modern world. Stereotypes are dangerous, yet arguments around co-education always stray into them.
It is generally agreed that children learn best among peers of similar ability - hence the high popularity of setting in secondary schools, state and independent. The separatists take that argument further, claiming girls and boys learn in different ways, so should be taught separately.
Back comes the counter-argument: are they not then disadvantaging those boys and girls who don't conform to the stereotype? Plenty of boys have a "feminine" preferred learning style - careful, painstaking preparation and lots of hard, neat work - while some girls prefer to work in the "masculine" way: flying intellectual kites, taking risks, leaving things to the last minute, relying on inspiration.
That focused, conscientious, hard-working all-girl environment can behave like a pressure cooker. Similarly, boy-only schools are too easily dominated by a laddish, macho culture which at its worst values only sport and gives rise to all kinds of bullying.
Any sane teacher will snort at those outrageous descriptions and say: "That doesn't happen in a well-run school." And they're right. It doesn't.
Perhaps the only reliable view was outlined in a piece of research published in 2008 by professors Alan Smithers and Pamela Robinson.
They looked into the relative success of pupils from single-sex and co-eds. When all the other variables were removed, these two eminent researchers found no significant differences. "A good school," they concluded, "is a good school."
I'm a passionate co-educationist. I don't shrink from confronting gender issues. I think my school's decision to go mixed was the most important change it has made in nearly five hundred years.
But that's just my view, and I won't force it on others: we heads should shut up and let parents decide.
Dr Bernard Trafford is headmaster of Newcastle's Royal Grammar School and vice-chairman of the Headmasters' and Headmistresses' Conference.