YOU personally did not take out the contract, so you do not have to pay it. Your dad does and he would have had to cancel it. If you continued to attend beyond the membership your father took out, then you do have to pay. It does not matter how often you went, if you went you still had a membership and have to pay. You use the gym, you have to pay for it.
If they are charging you, they had to have gotten your information from you right? As long as dad paid for the membership he started, then you still had it. If you intended to cancel what he started, you should have done it in writing. I suspect the dispute is with your dad and not you since he got it for you and paid for it as a gift. It would also depend if there was a term to the initial contract agreement or if the gym simply has month to month memberships. If you went you need to pay, even if it was only once that month, there is NO QUESTION about that. Something had to have been signed (by Dad) initially, so look at that and have the gym give you a written copy of their membership policies to see what the length and terms of cancellation are. I can not really tell you specifically not knowing what it says and what state you live in.
You are not personally liable for a membership Dad purchased and paid for, but if you gave them your bank info to make and take over payments, they you assumed the debt. Yes, they can indeed send you to collections.