-- a feeling of confidence in someone that shows you believe they are honest, fair, and reliable
-- confidence that something is safe, reliable, or effective
If this is pretty close to the mark, then "distrust" would mean that there was a confidence in the belief that someone was dishonest, unfair and unreliable or that there was confidence in the belief that something was unsafe, unreliable or ineffective.
In other words, distrust requires a trust that distrust is warranted.
Trust can rank pretty high on the totem pole of human characteristics. Politicians angle for trust; religions put themselves forward as trustworthy ... nobody, it seems, wants to be considered unworthy of trust.
And yet, I think, trust and its joined-at-the-hip sibling distrust, are worth a look. What happens to trust or distrust in the middle of a sneeze or laugh? Where do they go? How valuable and certain and trustworthy are they in such a moment? Does anything really deserve or require my trust or distrust? What happens when the exercise of trust or distrust is simply set aside for a moment ... when the capacities are still capacities, but the need to exercise them takes a breather? Does it own me or do I own it ... or either or neither or both/and? If I trust you or you trust me, does that make either of us more trustworthy?
I don't mean to criticize or disdain trust and distrust. Good and bad, silly or sad is not so much the point. But investigating cherished beliefs ... well, how about that? I'd say it's a good exercise. I might even say "trust me" ....
But I know you would laugh in my face.