I'm sorry you guys i didn't know where to post this question.
Well, by your reaction it sounds at least plausible that you might have had a trauma associated with your breasts, and sexual abuse could give you a reaction like that if it was specifically directed to the breasts. You say you like what your breasts look like ... do you also like what they represent in terms of being attractive to men, or does that idea make your skin crawl? Do you think your father would answer you honestly if you asked him if your mom's comment about possible abuse was true, or would asking open a can of worms and cause all kinds of problems for you, your relationship with your dad, and your mother?
I have heard of people getting hypnotized by a therapist who is medically trained in the use of hypnosis, to try to unearth buried feelings and memories. Maybe you could find a therapist some day who is trained in the medical use of hypnosis and has a lot of experience, and could go in to try to find out why you hate your breasts being touched. If you decide to do this, be sure to check references and go to someone highly recommended for their experience. You don't want the therapist to inadvertently plant a "memory" in their attempts to ask the question.
Good luck, I'm sorry that this is such a strong negative for you. Breasts should be just like any other private part, not laden with such a strong negative that you can't even touch them yourself.
Maybe the way it's being touched? I hate touching mine, but if I massage the breast and work my way up to that. I avoided breast play a d sort of still do. It just feels... Annoying? Ugly? I cant explain it really. But I found a breast massage is somewhat makes messing with my nipples tolerable.