If we want to attain inner peace, then we must first rid ourselves of noise. It is simple principle: the more noise you have, the less silence you have. The quest for peace means turning off the noise.
Forgiveness is a tool for attaining inner peace, since there is no other more powerful 'inner noisemaker' than resentment (with the exception of fear, but we can get into that later). A lack of forgiveness can rob us of all joy, peace, and inner stillness.
For this reason, forgiveness is main element in sobriety. No amount of therapy or medication can take its place. Addicts 'medicate' their noises with the objects of their obsessions, something everyone does to some degree. This is why death renders its own judgment: in death we enter into a place of silence, when we have our memories but none of the distractions we had in life.
When we become intentionally silent, then we discover the sources of our noise. The process of recovery is one of repeatedly entering into the silence to discover what it brings forth. When we are silent, we see that forgiveness is not so much for the other person as it is for ourselves.
If we cannot have peace, then we cannot have God. Christ promises peace to those who are united with Him, and so when we are not peaceful, then we are not part of Him.