Sexism isn't just excluding or discriminating,
Yes, it is, in addition to prejudice and stereotyping.
there is one other vital component: harm.
There is no dictionary that agrees with you on this point. I'm going to side with merriam-webster and oxford on this one, as would most people. There is no dictionary in the world that defines harm as a component of sexism.
It's like having a girl's bathroom and a boy's bathroom. The girl's bathroom might even have more facilities (tampon machines/disposal). It's not sexist because it doesn't disadvantage either gender, it's simply discriminating for a perfectly legitimate reason.
It's not discrimination, and there is no dictionary that agrees with your use of this word either. Providing facilities for physical differences has never been regarded as discrimination, as there is no exclusion going on.
Unless someone can show that this school will somehow harm boys then it isn't sexist.
Only if one uses your definition of "sexist". The rest of us use the the dictionary definitions. Redefining words to make your argument work is a sure sign that your argument is broken.
I cannot stress this enough: Redefining the word sexism to a meaning not found in any dictionary just to make your argument work is a sure sign that your argument is broken!
It would be easier, at this point, for you to change your argument than to ask every dictionary in the world to change the meaning of the word sexism.