This is a very common clash of interests. Your parents may regret or doubt the choices they themselves made years ago. But overall, they just want their own children to be comfortable and well-taken care of in their adulthood; they want to ensure that you make enough money to care for yourself, and that you aren’t needlessly struggling. I had the same conversation with my father in high school (he wanted me to become an engineer), and I remember friends and classmates having struggles with their parents over this (including watching a classmate melt down into tears when she told her parents she didn’t want to be pre-med anymore and they yelled at her over the phone).
If your parents aren’t paying for your education, then you need to make your own choices and give yourself some intrinsic support, or seek support in other places - like professors or peers or mentors. Or you need to be satisfied with more generic support. My father never agreed with my choices (getting a BA in psychology and a PhD in public health) because he didn’t understand them and didn’t see them as lucrative; but he still supported me as a person, as his daughter. If your parents do that, then you might have to learn to get along with that.
If your parents are paying for your education, it becomes more delicate - you either need to be convincing or you need to compromise. This is where the answer to your question comes into play.
It may not be helpful but both are important - to do what you at least like, and to have money. Which one is more important is more dependent on your own work style and lifestyle. I’m almost 29 and 8 years post-college, and almost 1 year post-PhD. When I was in my early 20s and had few commitments and tethers, I would’ve said that doing what I loved was way more important than money, and all I needed was an indoor place to lay my head and something decent to eat.
Now that I’m approaching my 30s and I have a husband and a network of friends who make good money and more commitments and desires to fulfill, I say the reverse…while I think it’s important to do what you like - or rather, to like and enjoy your job - I think that there are a lot of things that I’d be good at doing and enjoy, but I’d prefer to do the things that are more remunerative than the things that don’t pay well. After having lived independently for several years, and learned what kind of money is necessary to live in the kinds of places I want to live, buying the kinds of things I want to buy…there’s a certain amount that I’m not willing to make under and there’s a certain amount that I’d ideally like to make. But that’s MY work style. My sister (who is 24) would die if she had to sit at a desk all day and she’d much rather make less money if she got to be outdoors or in some other job that involves a lot of movement. (Appropriately, she works for a physical therapist.)
The thing is, though, I would’ve never known this about myself at 21 when I graduated from college, much less at 18 when I was picking a major. It’s the kind of thing that evolves over the course of your life and might change over time. The other thing is that your major doesn’t necessarily determine how much money you make and you can’t predict what’s going to be lucrative 10-15 years out. So you have to major in what you like, what you excel at, and develop skills that will always be in demand. Those are writing, presenting, other forms of communication, programming/coding, statistical and quantitative skills, other technical skills, speaking a foreign language (which one really depends on our geopolitical situation at the time, but most are pretty useful) and some others that I probably don’t know about. You don’t necessarily need to know ALL of them, or even most. But if you can develop one or two so that you are really good at them, and maybe learn one or two more to be decent, you have a good chance of making good money.