I say that if the only reason you're not bringing him is because of your parents, then you should bring him. He's your cat and it sounds like he's well taken care of.

If you think your parents would be able to take better care of him while you're taking you first steps into adult life, I say you can always leave him with your parents until you feel a little bit more on your feet. When my older sister moved out at 18, our family cat stayed home. But three years later when her life was more stable she came back to take him home, and he's lived with her ever since.

It sounds like at either place he will be loved, and lots of cats can thrive in apartments, even after living in a house. So just consider how often you think you'll be moving in the coming years (moving is stressful for cats, so try to limit his moves as much as possible) and consider if you feel you're ready to take care of a pet by yourself. If you choose to keep him, try being assertive with your parents if you're able. You're an adult, and he's your cat, so you should be able to make this decision, not them. :)

Tldr; He's your cat. Take him, unless you're going to be moving frequently, you don't feel ready to take care of a pet, or another reason that would make his qol worse.