After re-reading your question, appears to be some problems. Dad comes in to give you a present of 2 months of membership of June and July and pays for it. But if I had to guess your dad (actually) signed you up for a years membership that he was not aware of when he signed it, thinking I am paying only for 2 months to see if my son likes it and if so, then my son can continue to pay for the gym (each) month.
You continue to use the membership for August, September and October, but (no one) paid, thus they went after you to pay and threatened you for the $160 that was owed for the 3 months, which you paid.
But it was not until April that you realized that the gym had been taking out payments, thus you stopped it and then by June the gym was back threatening to sue you for payments owed, even though you have not been back to the gym since October?
For the gym to deduct payments means that YOU signed something allowing them to do this, since how can they do this (unless) you sign some kind of authorization?
The problem with gyms is that they need people to sign for (yearly) memberships, since many people get into this “I need to get healthy and exercise” thus use it a couple of months and (never) come back, thus they need the yearly memberships, that if you go only a couple of months, they don’t care and just collect, since you signed a contract.
My (guess) what happened is dad signed the (original) contract, thus they kept charging him, but he did (not) give any type of authorization to deduct this, thus unable to collect, then you keep using the gym, thus they went after you for the unpaid months. But when you did, then (you) signed a contract allowing them to deduct from your account, till you stopped it, thus now once again going after you if I had to guess for the balance of the contract.
So (if) there is a contract for 1 year, then tell them for you or your dad to pay, then you will need proof of the signed contract and if not, then no one owes them a dime. But be aware it still can go into collections and if so, then you would have to start over and dispute the collections.