I'm 19...guess that's not too old, but I'm definitely old enough to know right from wrong, and know my limits to what I can handle, and believe me, a ball python is not too hard to handle. I'll see what I can put together with my ramblings and you can let your mom read it if you wish...

They're small snakes really. Usually getting no bigger than 4 feet(5 feet is considered big and rare for a ball python) but most males max out at around 3 feet. They're not too thick, and therefore not a problem to handle. They aren't snakes that you have to worry about when you wrap one around your neck. If they squeeze too tight, you can just unwrap them with no problems. They're also quite simple to care for. As long as they have an appropriately sized tank to live in, with temps ranging from 80-85 cool side and 90-95 warm side, and humidity in the 50-60's, everythings good. Then you just have to spot clean here and there, and change water regularly. Of course, once a week they'll need a mouse to eat, but that's not expensive at all really. Maybe a dollar a week. And if you're worried about a ball python hurting you or anything, all I can say is a pet dog could do more damage to you than a ball python can. The most they can do is bite you, and they're nothing bad to be bitten by. You could compare it to a bee sting I guess.
If you have a phobia of snakes, ball pythons are perfect to help you get over the fear. They're very docile and laid back, so they're easy to handle. But as your son said, they're easy enough to care for and maintain, that if you really don't want to see or touch it, you won't have to. But I'm sure that after you've seen him handling the little cutie, you'll start to see how harmless and beautiful they are and maybe start handling it yourself. My mom is deathly afraid of snakes. She was traumatized when a kid in gradeschool shoved a garden snake down her back. But after she realised I'm serious about owning a snake and after I started talking about them enough, she realised it'd be fine to have one in the house. Since then she's even asked me questions about them often and learned some stuff about them herself. She's even said she'll probably pet little Pelota when I get her this month. Anyway, all I can say is you should seriously reconsider letting your son own one of these beautiful creatures. They're a great learning experience, and you can really start to appreciate and admire different types of animals instead of the usual pet cats and dogs. If you or Mike have any questions, don't hesitate to ask. There are plenty of people on this site that know what they're talking about and can help you out. I may not be the most knowlegable with ball pythons, but I know enough to know it's a great pet to have, and I know if I had a son or daughter, I wouldn't break their heart and tell them they can't have one.