Gonna have to disagree with you on several points:
1) It is about the age. If you are not of the legal working age, then you are not legally able to work in a taxable wage position. This does not include areas such as lawn care, babysitting, or dog walking for the neighbors.
1a) Restaurants and theaters have to think about liability, and their customer base. Do you have insurance? If not, will the restaurant cover you if you damage something, or god forbid, someone? What if you insult a customer, either on purpose or accidentally? Are you prepared for the backlash when the restaurant owner/manager blames you specifically for the person walking out without paying because an employee was rude/immature? You could cost them that customer, plus countless others from negative publicity.
1b) Situations. I have yet to meet a 12-15 year old who is mature enough to handle many situations that arise in performance situations? I won't go into detail about what those are.
2) Experience. Sorry. I'm not going to hire a child to entertain me,my children, or my customers. End of story. I really don't care if they are David Copperfield reincarnated. You are a child, and I'm not going to hire you. Period.
3) Maturity. 'Nuff said. You just told us you argued with your parents about this for two hours. A child who argues with their parents over things that the parents could be held liable for does not seem, to me, to be exhibiting a level of maturity that is professional level.
I will agree that when not to do magic is when your spectators are thinking about other things. Contrary to popular belief, not everyone wants to see a trick when you want to show them one.
Just my two cents and 20 years worth.