Mary, a focal asymmetry means the mammogram shows an abnormality, but it's impossible to tell what's causing it. You've since had an ultrasound, which ruled out cysts and solid lesions; and the mammogam apparently showed no evidence of microcalcifications, which can be an early sign of breast cancer. Still, it's not clear what's causing this asymmetry (which is basically the breast tissue being distorted for some reason). Thus the doctor's desire that you have an MRI, which is more sensitive than a mammogram, and would be able to show more clearly what's going on.
I'm sorry your insurance won't cover this. Perhaps you could get your doctor to contact the insurance company and explain the need for it. Or, s/he may just be jumping ahead to a biopsy, without the MRI - since you're seeing a breast surgeon. Please don't panic about having a biopsy - about 85% of breast biopsies are negative for cancer, so the odds are on your side.
You really should do what you can to find out what's causing this abnormal mammogram. And don't compare your experience to your cousin's; this is probably NOT breast cancer, and you won't need your breast removed - but you absolutely have to rule cancer out, which means further diagnostic testing. So do what the doctor says, and see the surgeon, OK? I hope you get good news, at the end of all these tests. Take care- PJH