Trust is key to a relationship, any relationship. When you can’t rely on the truth of what someone is saying, then you really can’t be invested or dependent on them.
Broken commitments can be just as damaging as deliberate mistruths. If someone blows off a commitment too you, then how can you trust them to keep further commitments to you? How can you put yourself in a position where you need to rely on them?
Sometimes it is unavoidable, you make a commitment you didn’t really think through, or you have competing commitments. It takes bravery to address that, but if you want to preserve the relationship, then you need to need to own up to the situation as soon as you realize it and address it directly with the individual you are breaking the commitment with, probably best in person.
Commitments are critical though. Consistently meeting commitments, and allowing yourself to be dependent on someone else’s commitments is how you build trust.