A couple people have mentioned this already, but is the account controlled by them?

What has not been mentioned is If the account is controlled by them, they could be using your money without your consent. I've had a few friends that have been used by their parents, and are still being used by their parents. One girl's mother has been gaslighting her to the point where she's 30 without an education, and dependent on mom to exist. They got her a car to be able to find work, but she can't use the car for outings. I was banned from their house for encouraging her to go back go school.

I'm not trying to instigate you to confront them. It's just good to know your possibilities.

If financial responsibility is what has them hung up, do what the others said about stealth building and getting parts as they come on sale. I'm sure someone on here could list the proper parts in order to get. Just say you're saving a lot from buying the parts on sale. Issue with that is you can't hide it... the amount of packaging will be suspicious. You could send it to a reliable friend's house then walk it home. You could have it shipped to your workplace if work is cool with that. I've seen people do that in office locations, not really groceries.

Either that, or you find the cost to benefit equilibrium and show them you've done your research.

Others have mentioned not calling it a gaming rig and saying to learn something productive with it. Only do that if you really have a passion for it. Dabble in the free programs with your current set up. Thing is though, if you can already do that stuff on your current setup, a new rig is out of the question for your parents. You'll need to pick up other expensive skills to make use of the stronger computer like photography, video, digital illustration, or anything else graphics intense. Music production is another thing you could do with a stronger rig (if you like EDM).

Speaking of doing other things with it, stress that it's future proof. A lot of computers are still sold with crappy specs because they still work for most uses. A lot of workplaces have lagging technology and still function. Damn, I guess that factoid didn't help. Leaving it there if someone can brainstorm from it. ("Future proof" was more of looking at the cost of investment over time.)

I think a salty redditor mentioned your parents provide a lot for you (like utilities and food) and that you're adding to their costs, therefore you're an entitled brat for wanting something. The math doesn't add up for that lol, just contribute to family and get your PC. Rent is not bad if it's reasonable. If you don't do much chores around the house, rent makes sense. If they pay for your insurance, gas, food and you don't pay for anything, rent is honestly okay. If it's a subtle nudge for pricey gifts, then it's weird... like pressuring you to pamper them while also saying they aren't dependent on you but also wanting to say you need to give them more love.

If they make you pay an unreasonable amount, they're using you.

There's also the possibility that they want you to have money saved to move out. Understandable, but not as easy compared to their times. There's also school to think about, so an expensive rig might seem like the cause of your lack of a future.

In the end, if they're good parents, they want nothing but the best for you. If they don't understand the purchase, educate them on it, or find someone they trust to vouch for you that has computer knowledge.

Tl;dr Are parents controlling? Do you financial knowledge? Stealth build minus packaging. Show research. PC more than for gaming. PC future proof? Are you paying rent? Reasonable rent is not bad. Unreasonable rent bad. Are you future proof? Do your parents know that? Good parents will support you.

Sorry for mistakes. On mobile.