How to I prove to my parents that I am mature enough to do things myself?

I’m ready to start doing things myself, like doing my homework without someone checking it and making breakfast without my mom standing over making sure I don’t burn anything. Or even just doing my laundery without my parents watching me making sure I don’t do anything wrong. Every other kid my age is able to do all of this alone. When I ask to do these things myself, my parents tell me that I have to prove myself responsible enough first. The only problem is, if they won’t let me do these things without help, how can I prove I am responsible?