Why is it called Off the wagon when you stop drinking alcohol?

You have this wrong

When you stop drinking alcohol you are said to be ON the wagon.

Thus if you fall OFF the wagon it is taken to mean that you have started to drink alcohol again having one stopped.

The WAGON in the expression relates to the water wagon, which was a horse-drawn water car once used to spray dirt roads to keep down the dust. (So if you were on the wagon you must be drinking WATER).