Except all the places we do (single-gender schools do exist, and even in non-single-gender schools physical education and health are often taught separately).
Also, maybe we should do more of this; there is some evidence in the literature that at some ages educational outcomes would be better with gender segregation if we did things right in terms of keeping equality of resources. Which is of course the sticking point.
> why should we segregate them on the basis of one year age gap
In case it wasn't clear from my answer above, I don't think we should. I think we should group kids by interests and current level (i.e. by what they will be trying to learn) a lot more than we do now.
I am saying that there are some studies showing gender segregation at certain ages may improve educational outcomes, largely depending on how it affects teacher behavior. Whether that means we should do it rather depends on whether we can get those teacher behavior effects in other ways and whether gender segregation would cause other issues (e.g. unequal resource allocation).
For some specifics that are pretty easy to find, see http://econweb.umd.edu/~turner/Lee_Turner_Gender.pdf for recent evidence that boys do may do better in all-boy schools, at least in some cultural contexts. There were a bunch of studies in the '90s that claimed girls do better with no boys in the class, due to teachers actually noticing them, but that effect seems to have more or less disappeared over the last 20-25 years.
In general, as in all things to do with kids and education the answer is almost certainly "it depends". Some children do better in a gender-segregated environment. Some do better in a gender-integrated one. Some don't particularly care. Hence all the caveats above about "some" and "may" and so forth. The hard part is figuring out when gender-segregated education is appropriate and when it's harmful, on a student-by-student basis. Unfortunately, public education is too cookie-cutter for such details.
Except all the places we do (single-gender schools do exist, and even in non-single-gender schools physical education and health are often taught separately).
Also, maybe we should do more of this; there is some evidence in the literature that at some ages educational outcomes would be better with gender segregation if we did things right in terms of keeping equality of resources. Which is of course the sticking point.
> why should we segregate them on the basis of one year age gap
In case it wasn't clear from my answer above, I don't think we should. I think we should group kids by interests and current level (i.e. by what they will be trying to learn) a lot more than we do now.