I think you're kiiiiiiind of The Asshole Here. I don't think you're being malicious, but it's easy to be ignorant of your class. I think you are probably a nice guy but let me try and angle this problem so you can empathize with her a bit. I don't think its breakup worthy, but you should probably approach your girlfriend with an olive branch, apologize and try to dig deeper onto why she is upset, specifically. FWIW I'm a mid-30s man who grew up poor in the USA and am now a comfortable STEM professional, I can dig both sides of this.
You feel that you and your girlfriend are 'equal' because you are splitting things 50-50. But you're not equal, because if you run out of "your" money, you will have infinite safety nets to catch you, including a job and trust fund that ensure you will never "need" to be successful at any career to live comfortably. You are honorably trying to earn your own wealth, but the fallback income you possess enables you to take exciting risks to pursue your passions. You may find success in a variety of cool fields like biotech or video games from your engineering degree, or you might not end up as an engineer but find success in another field. All along the way, you will have the psychological safety of knowing you will never be in danger of homelessness, or even basic hardships like not being able to save because you have to carefully balance utilities costs.
She is trying to escape generational poverty and spending essentially all of her money on this gamble, that being a doctor is going to provide her financial stability she has never had. She might need to rely on this to work out, because her family might need her to for their elder years care. No matter how equal you are in your day-to-day life, that's because of what she assumed was a compromise between two people who were both taking a bit of a risk with their life.
Only to find out you aren't taking the same gamble. Not even close, you are basically living your whole life, now and into the future, with Monopoly money. And while morally or ethically she's doesn't have a claim to your money, your approach of strict 50-50 with someone you know is struggling, is kinda like when college guys go through a Nietzsche phase of being "totally honest" which helps them cover for being callous in relationships. (I did this too) If you are worried about trust-gold diggers, I think it's natural after a period of time to extend some of that financial leverage as a sliding scale towards marriage. This could form a natural progression of covering more housing expenses when you move in, but keeping groceries/entertainment still 50-50.
You wouldn't be paying 50-50 after marriage, while trying to start a family right? So at some point in time your financial privilege can and will impact your personal life (for example, withdrawing it to start a business) and thus your relationships, you just need to have some terms in your head of when that happens. Instead of keeping it locked away in a jar, which also puts off your responsibility thinking about it, you should probably think about how you
I don't think you or your family are jerks, but about ten years ago I dated a woman way, way out of my financial class. She wasn't mean, but she did not fathom how I ever had to make sacrifices or tradeoffs due to money or work requirements, because they never interfered in hers. I can imagine your girlfriend is a little miffed that you are basically pretend-struggling while she is legitimately risking a lot trying to get ahead.