Well, it's not like diet soda (or regular soda, for that matter) is a REQUIREMENT FOR LIFE or anything. Meaning, stop if if you want to, and see if it makes a difference in your overall health.
But the "reasoning" behind your son's plea is that there are folks that claim that aspertame is the culprit, that it leads to all sorts of health problems including neurological problems, and so stopping consuming aspertame will create instant health in all sorts of people with diverse health issues.
Whenever I hear these claims, I go to Snopes, which researches and proves...or debunks..the rumors. Here is their report about this:
...I am not a doctor, nor health professional, and don't pretend to be one, here.....