Did you read the contract before you signed it?

If yes, when you made a conscious decision to break it, you should be responsible for consequences.

If no, you should know that it is your responsibility to read a contract before signing it. Again, you should pay for the consequences for not reading it. Now you know that it is a "very substantial" amount of money, do you still want your kid go to another school :-)

The only circumstance I can think of that you may break a contract for free is that you did sign it at your free will (e.g. someone was holding a gun to your head ;-)