As you know, St. John’s University is one of the few remaining Bachelor of Science Physician Assistant Program available in the US. Most have transitioned to a Mater’s level program and are VERY competitive to get into, given the large pool of applicants who wish to pursue a Physician Assistant career. I think your parents might be concerned that a pursuing a degree in Biology and not getting into medical school might leave you with very little career options. I have seen so many “Premed”/Biology graduates who failed to gain entrance to medical school are “forced” to seek another undergraduate degree in (for instance) Nursing or other healthcare-related degree. In the case of nursing, these graduates have to spend another 1 - 1.5 years doing prerequisites just to gain entrance to an accelerated BSN (or ASN) program (1.5 - 2 years).
If you are fearful of low grades in a PA program, then one would be concerned about your ability to be successful at gaining entrance to an MD/DO program. There are other Physician Assistant Programs in the NYC, if the St. John’s University program is cost prohibitive. CUNY-CCNY has a PA program that was also a 4-year program, but they have now transitioned to a 5-year BS/MS degree program (better than other PA programs which requires an undergraduate degree for entrance to their MS PA program, which typically last 2 - 2.5 years).
I think you should stick with your PA program, although you will in all likelihood, have to take a number of prerequisites needed for medical school after completing your PA degree. A PA degree is a good fall back position in case medical school doesn’t pan out.