Well, in my country, it's mandatory to go to school until at least 16. Not that the government will let you down, but past 16, no school is obligated to take you (unless you fork some money) or you can make your case that it was totally not your fault (long illness, bad parenting, etc...). So, a 23 years old, -working- highschooler is really unlikely.
Here, I think it's just an absurd twist added in to poke fun at the age gap trope.