How to deal with the fact that people are imperfect?

Recently I've had a few major life events occur, namely a breakup and problems with my family. It's occurring to me more and more that people in general are not to be trusted. Every single person I've known in my life has let me down when trusted with important things. Parents, siblings, friends, partners - they've all without exception lied and betrayed my trust at various times.

The only people I feel really positive about are casual friends and work colleagues, and I put this down to the fact that they're at arms length so to speak. They're can't let me down because I haven't entrusted anything big to them and so the stakes are low.

Even myself - I would say I'm sometimes unreliable, greedy, selfish and have lied to those I love. I live alone right now and am very independent, and I feel a general unwillingness to interact with anyone on a deep level right now because of this feeling of distrust.

Does anyone else feel this way? I don't want to but it just seems like something that's staring me in the face right now. How do we overcome this? How do we accept that everyone we let get close to us will one day let us down?