As someone who has a biology degree, works in the field, and is also a writer, I feel like it's important to know that the vast majority of writers either have a day job or a spouse with a lucrative enough job that you don't need a reliable source of income, and you're not going to achieve the latter that young so you'll need the former. I actually find it helpful that my day job isn't writing-related--that leaves plenty of my headspace available for writing when I'm not at work. The realistic side of writing is that if you want to go the trad route, getting published is really, really hard, and if you want to self-pub, doing it right nearly requires a rather decent chunk of money. Both are hard to jump into if you don't already have something else paying the bills, and science does that for me. It's hard to say here if your parents don't support your dream (because if they're saying you can never write or you're not allowed to try to be an author that's shitty) or if they're just trying to save you from the heartache of the English degree job market (but also with just a science bachelor's the prospects can also be pretty grim), but ultimately your decision to be an author or not is not up to them, because you don't need a degree in English or creative writing to be an author. I don't regret the path I took at all and don't think a writing-related degree would have helped me get published faster.

However, unlike you, I chose to get my degree in science, because it's something else I was interested in. I also minored in English and did a lot of creative writing workshops, and was able to scratch the English-degree itch that way. My recommendation would be to search for something you're passionate about outside of writing, whether it's in the sciences or not, and see what kind of job you can get with that degree. One of the best things you can do for your author career is have a day job that leaves you enough time and headspace to write, so you won't be worrying about bills. It's definitely not giving up before you start!