Roots of sexism

I read an article by Holly Baxter in the Guardian, "School uniform policies are bad for all students - but especially girls" and it got me thinking about Sexism, which made me realize that maybe it starts in school.
School is meant to be a temple of knowledge or an information bank that prepares you for the real word. I can easily counter that and say it doesn't prepare you for the real world because that world is very different from what we learn in school, and I'm talking with experience because I just finished interning about three weeks ago.There are actually many flaws in schools but coming back to what I was about to say: this temple of knowledge not only supplies you with useless subjects like chemistry and topics like Pythagoras theorem while leaving out how to apply for loans, but it also enforces Sexism.
The first thing is all the boys vs girls games or making the guys play on the field and the girls in the swings area. My sister wants to play football but apparently the sports teacher says that girls aren't allowed. What is that supposed to mean? Who brought in this gender barrier in sports? These kids just learn to let guys do the playing on the field.
The second thing is the uniform. Girls are meant to wear skirts and shirts. Now, the skirts can't be too short because they will look 'inappropriate' and make guys stare at you and not too long because those aren't normal. Why do we only focus on training girls to be careful of the fine border between pretty and revealing and not train guys to control themselves? Teach them not to stare, this isn't supposed to be a patriarchal society, it's meant to be equal.
Third, teachers expect guys to submit their assignments late and to not be able to sit still in class. If a guy hands in an assignment three weeks late, it's ok, but if a girl does that, it's not ok. If a guy talks in class or disrupts the class, teachers dismiss is saying "boys will be boys". But, if a girl does the same, she will receive a scolding. We aren't perfect, teachers. Please remove the saying "boys will be boys" and expect more from them too because this is very sexist.
Fourth is the length of hair, at least over here in Indian schools. Girls are expected to keep long hair and guys are expected to keep short hair and it comes under uniform. This one really bothers me, why can't we decide what length we want? At least they are liberal with girls and let us keep short hair, but they won't let guys keep long hair. What's worse is, if a guy keeps long hair, people just say "he has long hair", but if a girl keeps short hair, people say "she has a boy cut". What on earth is a boy cut? I got bored of long hair and cut it short to a pixie, and people ask me, "Why do you have a boy cut?" What makes you call short hair a boy cut? This sounds so sexist; we really have to get rid of this term "boy cut". But I know it's part of the culture in school, a culture enforced by school which claims that the ideal guy has short hair and the ideal girl has two long plates.
Anyway, I think I have created enough controversy for now, so adios.