I trust everyone to be exactly what they are. You can trust anyone to be what they are - in that sense, everyone is trustworthy. The trick is in knowing what they are.
And so, when someone "betrays your trust" what has really happened is that they have revealed something of who they are that you didn't know before. They have challenged what you thought you knew of them. They were never responsible to be the person you thought they were. They were never responsible for the trust you placed in them that they would be different than what they are, would be what you hoped they were. That was always your responsibility.
That was always MY responsibility.
And so, my responsibility becomes knowing people better, learning who they are, so that I know how I can trust them to be, to act, in situations in which we are likely to find ourselves together. In this way, I grow my trust, but it is not trust in the other person, it is trust in my own judgment of what I can reasonably expect from them. I have always trusted them to be exactly what they are - now, I need to trust myself that I know them well enough to guess right, and entwine with them, count on them, appropriately.
Knowing that, in any case, most of what I see is simply reflection.
And that will do, for now.