I'm a current programmer and I also got a Master's Degree in computer science back in the day.
In my experience for the job market the degree is basically just a credential: It's non-employment work experience that can get you hired to your first job. It worked for me in that regard, but even 1-2 years into my career companies stopped asking me what I did at University.
There are however many other ways to show off entry-level credentials. Contributing code to some FOSS project, interning, taking a MooC or a coding camp would all accomplish more or less the same thing. None of these cost as much as a student loan. And after getting a job this sort of experience will cease to matter for employers.
Today personally I'd be a bit ambivalent about even getting a BsC instead of doing those things, considering it's basically just an entry credential and the other ones are free or nearly free.
MsC I would definitely not recommend just for employment purposes, it's not doing anything for you the BsC won't. If your son is curious about becoming a computer scientist he can take a MsC, this will give him a good idea about what research in the field looks like and if that'd be any fun to go into.
Computer science basically becomes "applied mathematics" at the research level. Personally I decided that was not what motivated me, but I'd rather make things with code, so I didn't continue after finishing my degree. But if he's double majoring in math he might find that more enjoyable than I did?
