It is important for ME to be trustworthy because I value the trust others put in me.
Having worked with abuse survivors I realized what an honor it was to have earned the trust of people who had learned to trust no one.
Trustworthiness is more than not telling lies. It is a pattern of behavior that others can rely on. No one can do it perfectly. And life sometimes gets in the way. But as much as possible I think we need to meet our commitments and responsibilities. Many of those commitments ands responsibilities are never spoken. We shown that we are trustworthy when we behave responsibly towards others regardless of what happens. I'll give you an example:
When my mother caught my step-father sexually abusing me I expected her to be trustworthy and protect me. Instead she sent me away from the family and into foster care a five hour drive away. I didn't see my family for another 3 years. She says this was her way of protecting me. Keep him in the home and get rid of me.
Parents don't need to tell a child "I will care for you until you are grown." It is a given. My mother abandoned me when I was 9 and I didn't see her for almost 3 years. A year later she abandoned me again for another 3 years when she sent me to foster care. Its really hard to trust a person when they keep getting rid of you. And I'll tell you I spent a lot of years doing everything she wanted after that so she wouldn't get rid of me again. But she did.
If I was (remote possibility here) to reconnect with her I don't think I could ever trust her again. Sooner or later she would find some pretense to get rid of me again.
So I know what being untrustworthy does to a person. I don't ever want to be that type of person.