They want to teach you how to spell, etc., not download crappola.
Not being an uber prick here, but, if you're going to be all "teach you how to spell", don't you think correct grammar would be a start?
But the reason schools, and other public services won't let you use p2p software is because they don't want you downloading stuff. Simple as, really.
Also, if you downloaded something illegal, using their connection, they are liable. That's the main reason why people should be a lot tighter on their home wireless networks.
Basically, it boils down to them not wanting you to use their server space, and their bandwidth to download your *censored* teen *censored* pr0n.