It is true that enrollment in undergraduate CS is highly volatile as potential students alternate from wanting to get in on the gold rush and then they hear arguments like those from your parents, which do have the kernel of truth that computer people face a "glass ceiling" in many organizations.

CS is an unusual academic field because it is situated between math, engineering, and other things. Part of it is focused on the hardware and software prevalent on Earth today but much of the theory is universal.

If you take CS I would suggest doing a dual major with math, you probably don't need to take many additional classes.