I think you have to look at putting your trust in someone as a risk. An emotional risk. And it can be a good thing if the other person knows that you're counting on them to honor your trust too, because it can build quite a close relationship, a special relationship.
It's interesting that you ask 'does anyone not trust anyone?' because I've wondered that myself. I think the majority of people are afraid of being hurt, and that's only natural. It's the same with me, as well.