Thanks for your question. I'm sorry that you are unhappy. You are not the only person who does not want to have breasts. There is no medical reason why you cannot have the breast tissue removed, but it would not be covered by insurance. Please also realize that it is a very ultimate decision in that you can't just go back later and place an implant if you are unhappy with the decision. Best of Luck!
Breast removal in a woman is most often associated with breast cancer treatment (either to remove the cancer or to match the other side). It may also be done for pain control. Breast reduction can be aggressive and still leave a recognizably female breast. All other reasons most likely are related to body image and gender identity. These are subjects that should be discussed with a mental health professional with a clear plan in mind before considering surgery. That said, a plastic surgeon may certainly remove breasts in as aesthetic manner as possible.
The question to start with is are you male or female? If you are a male with breasts (gynecomastia) then wanting them removed is entirely normal and reasonable and most plastic surgeons feel comfortable doing this.
If you are female, I would ask why you do not want breasts? Most every woman with A-cup breast that I have met in my nearly 30 years of surgery has wanted larger and more noticeable breasts. So the fact that you want no breasts at all is not at all normal. Are you afraid of cancer? Are you dealing with issues of gender dysphoria? These are the important questions which must be answered and dealt with before any surgery is contemplated.
Best of luck.