<snip>...everyone in my family has done alot of major business deals and none of them based their lives on computers. <snip>... they seem to think that a person can do anything with their brain that a computer can do.
You stated convincing them isn't a priority of yours, but if big business is what they consider worthwhile,
http://www.fortune500s.net/fortune500-list.php this is the list of the fortune 500. In the A's there were at least 7 companies whose sole business is in computer hardware or software, and more that depend heavily on computers. That roughly extrapolates to 175 or so on the whole list, or about 30%.
On the last point, a person can do anything with their brain (and much more) than a computer can. We wouldn't have AI research if that weren't the case, it would be solved. The thing is a computer can do things like math or physics a lot faster than a human. A human can explore a lot of things in parallel that may be more difficult for a computer, and sometimes this means the human can beat the computer at certain tasks. We can't program a brain to do specific computations with the same precision as we can with a computer, though.
If we had to map the human genome with just humans trying to link together and decode the chains, we'd be waiting a long time. With the computing available with the Human Genome Project began, they expected it to take many years. As the project went on, computing power increased greatly, to the point that they finished years ahead of schedule. It took a lot of smart people's brains doing a lot of work to write the software, determine the algorithms to use, etc., without which none of that would be possible. However, those smart people couldn't have finished within their lifetimes without computers.
Perhaps none of this would phase them, and your parents would still think this is all just a trend. It could be the case that even if you pursue it and get a good-paying job in software they still won't think it's worthwhile, but sometimes you have to just do what you know if right for you. Hopefully even if they don't understand they'll still support it because you're passion it about it, but be prepared to forage ahead without them.
-Lee