Wow thanks for the links I'll definitely show them that.
But their main argument is that actuaries have to find employment and that they will always be under someone of higher position unlike doctors and lawyers. I reckon if I can rebut this argument I will be much closer to persuading them.
I don't really know in detail what medicine is like, but I would have thought that most doctors would always be working under someone in a higher position? Like wouldn't GPs be working for their clinic? My knowledge of hospitals really just is from Scrubs... but they all work for the head guy, who would have worked for years to get to that elevated position. I guess for any job you could work hard for years and work your way to the top. I really don't understand what point they're trying to make. It seems a bit flawed to me and should hopefully be easy to rebut.
I'm sure you could find examples of programmers, mathematicians, artists, physicists who became head of a company. I'd imagine a lot of actuaries might go on to become CEO's or something like that.
Edit: As an actuary, couldn't you one day start your own actuarial consultancy firm? Like I don't think many doctors could split off from their employer and start their own business.