People speaking in absolutes about how this doesn't do a darn thing security-wise are missing part of the picture. Context menus are dynamically driven based on whatever you happen to be clicking on as well as the current state of the system. In most cases context menus are disabled because a good portion of the functionality provided within them is disabled. Right click > Properties: "Alert! You don't have permissions to do xyz" is an awful experience.
In most cases (I can't speak to your particular case because I don't know the details), the context menu is disabled because most or all of the actions within are denied via things like AD group policy. Given that you're talking about school computers, I'm guessing the admins don't want any personalization whatsoever so they disabled modifications.
The disabling of the context menu may simply be a side effect of a larger security policy.
The assumption here though is that they are actually disabling some of the underlying actions, not just the context menus.
Then again, it may not even be a security measure at all. It may simply be removed as an attempt to reduce the confusion of a non-tech savvy user.
Operative word being "attempt" of course... as you mentioned it frustrates such users.