I'm sorry to hear of your frustration.
Different airlines operate different policies but I know that some require flights cancelled within the 24 hour period after purchase to be cancelled on the phone for a full and immediate refund. Not sure how AA does it.
Usually, when you are cancelling, you are not cancelling the ticket as a whole, you are cancelling your booking on certain flights. For some tickets it is possible to not have any flights (because your plans have changed and you have cancelled them) and then you have up to one year, to find and fly replacement flights (with appropriate change fees and fare differences paid by you, of course.)
How is it legal? I suspect it's all in the fine print (usually terms and conditions, and fare rules) that one agrees to when one purchases the ticket (but very few read, and even fewer understand.)
It appears that airlines are usually a littler slower to return money than to take it - they like to keep that working capital. Actually that applies to almost all businesses.
I imagine you will get your money back in full (assuming the ticket was fully refundable and/or you have met other full refund requirements!)
rb211.