Holy sexism, batman! Okay, clearly some folks aren't comfortable with boy babysitters, but I say that's their problem. Unfortunately, you will have to explain to your son that some folks are biased, but we all have to explain that to our kids at some point, regarding some situation. I think it's TOTALLY FINE for a boy to babysit. My DH did when he was a teenager, and I'm sure he was great at it, just like he is now a great dad. Seriously, if folks have no issues with hiring a girl to sit for boys, they shouldn't have issues with a boy sitting for girls. Irresponsible kids come in both sexes, as do responsible kids. You CERTAINLY don't want to teach your son that the world EXPECTS boys to be perverts!!!!!
As for the age, I did start sitting when I was 12, but, as you said, only for kids on our street when my mom was home, and only for older kids (like 6 or 7) who couldn't be left alone, obviously, but could also do a lot for themselves. At the same time, I started working as a mother's helper for my godmother, who had a 6 year old and newborn--so I got experience helping with the newborn, but was never left alone with him at that stage. I started babysitting for a wider age range, and kids who were farther away (like, a 5-10 minute drive) when I was 14. I think the classes and certification are key, and also making sure he gets experience somehow while supervised (e.g. as a mother's helper, or with younger kids in the family).
BTW, I think it's GREAT that your son wants to work with kids. Many boys and men, I believe, are naturally caring nurturers, but our culture tends to discourage that--to the detriment of the boys, men, the women in their lives, and their eventual children. I hope you encourage your son, and help him to find families who are open to benefiting from his skills!