There's a difference between wealthy and rich. Bill Gates is wealthy. You're educated professional may be rich.
So how do you get rich?
So, if you choose Law, for example, it is a little bit more difficult. You can do extremely well, however, one must follow the correct path. You MUST go to a top law school. That is non-negotiable. Intern, Intern, Intern whilst there. Consider getting anything International and sitting for the bar exam of England and Wales if you're American. If you're qualified you will get a job at BigLaw for somewhere in the $200 000 K range as a first-year associate. Now, it's not easy. However, that's one path.
Additionally, one can get an MBA and/or work in Finance, which I'm not as familiar with. A lot of people on Reddit think earning six figures is rich. But, you can easily earn that if you have a professional degree from a decent school.
As well, there are the many savings advice given in the rest of the thread.
TL;DR: Go into law or finance with a degree from a top-rated school. You'll be making more out of school than your "MUh STEM" engineering buddies.