Such sentiments are certainly true, if the person involved in breaking trust, possesses little to no sense of repentance; nor a sincere ability to ask forgiveness. And so many are indeed guided by pride; perhaps seeing apologizing as a weakness rather than a strength. Life is simply too short to put up with such folks.
However, I do think true forgiveness is a very necessary part of life. It is often required; most of all, for our own personal healing.
Otherwise, the constant presence of the pain that person's transgression caused, simply continues to hurt and deteriorate us. Even though their carelessness or abuse has long since passed or ended.
I've often wondered which was more challenging? Truly forgiving someone; or teaching a person to ask forgiveness that has never understood the real nature of sincerely offering an apology?
I find it near impossible to offer forgiveness to those who have little to no concept of repentance. (Meaning they never actually ask to be forgiven.) But I've still had to slowly try, in many situations; over the course of many years; in order to more effectively move away from the pain their ignorance originally caused and the trust they broke as a result.
In those cases the trust is typically very permanently damaged!!!