First of all, this conversation can go a few different ways based on a few different factors.
First, you dont state if you are male or female.
Second, you dont really give much detail as to why your parents are opposed to the idea.
Third, are they concerned that higher education is going to A: bring down the family name? B: make you unattractive to shadchanim C: fill your head with ideas that will make you want to escape from the community.
Also, you are correct that the “yeshivisha world” does look down on professionals in some cases. But then, when they need a professional, they tend to look for some one heimish. It’s quite a contradiciton, they would never allow their children to be professionals, but when they need one, they prefer one of their own kind.
Dont let this discourage you. Ultimatley it is your life and there are many shining examples of religious doctors,lawyers,accountants,stock brokers, and business owners. Dont let yourself be pushed into a marriage and a lifestyle with a self perpetuating cycle of poverty that seems to be pushed as the only option.