Many people are put off at first by the 12-step thing and the jargon people use at meetings. If you could try a couple more meetings and get past that, it would be worth it. BuT if you can't, you can't.
well I went to an OA meeting tonight and OA is not for me. I think OA is a great program for some people but I am not one of those people. I have nothing against OA but I could tell I would not work well with OA and the whole "12 Step" thing.
I don't know anything about your relationship with your dad but if he takes you to your therapy he seems to acknowledge your problem and want you to get better. If you explain that this is another source of support, is free, and would really help you, why would he object? Perhaps you can tell him your therapist recommends this as well because I assume she does! If you worry he will be annoyed at having to take you somewhere else you can tell him that after you go to a couple meetings you will probably be able to get rides with other OA members.
OA is a great organization and you have no idea how helpful it will be to meet other people you can relate to, and in time, hopefully get a sponsor to work the steps with you and to call when you feel like binging. There is nothing like the support you will find there! The first time is the hardest, but trust me you will be made to feel very welcome!