I agree with your parents.
Info on possible job opportunities:
Apparently, without an advanced degree in that field and THEN an attempt at going into more advanced fields (like chiropractic, physical therapy, physician assistant, podiatric medicine, and osteopathic medicine programs in addition to medical, dental, optometry, pharmacy schools), you seem to be limited in what you can actually do with a simple BS degree in that major.
If you are going into one of those other fields, I think biology or pre-med would help you become more prepared anyway.
What is it you actually want to do as a career choice? If you don't know, why limit yourself?