There's a story often told to entrepreneurs about how elephants are trained to stay on a rope.
Elephants are powerful creatures - they could snap a rope in a heartbeat. Yet, trained elephants can be tied to a post or led around with even a terribly thin rope. So why don't they break free?
It's simple: from birth, they're tied with chains (which they can't break at that age). It is ingrained into their brain that "tied up" == "can't escape". Thus, when they are tied up with mere rope, they assume it will behave just like the chain, and they'll be stuck - so they don't even try.
People often behave the same way with computers. Several bad experiences with trying to fix something themselves, and making the situation worse, imprints them with the belief that they will never be able to fix their computers, and it's much better to simply let someone "who knows what they're doing" (as if we always do) handle it. Add to that the fact that if they try to fix it themselves, they may not remember everything that they tried and could possibly have caused a problem that would render solving the original problem much more difficult, and the fear (real, honest-to-God fear) much more understandable.
To stand further atop the shoulders of giants in this comment, I'll bring in a well-known (in this neck of the Internet) quote from Arthur C. Clarke: "Any sufficiently advanced technology is indistinguishable from magic". When they have to decide if they can fix it themselves, they are basically asking: "Am I a magician? No -> Okay, I'll take it to someone who is."
One thing I like to keep in mind in situations like this (to stay humble and avoid coming off as condescending) is that if I had a hardware failure, I'd take it to the Apple store right away. No f'n way would I fix that myself - why? Because I'd probably make it worse.