Is it always possible to forgive?

For some, perhaps. Certainly not for everyone.

It is absolutely possible for everyone to forgive, although many people refuse to, not realizing that by doing so they only harm themselves.

Forgiveness has little or nothing to do with the other person. It has everything to do with the one forgiving.

Look at it this way: someone has caused you harm, and you can either forgive that person and put to rest any continued harm, or you can harbor ill feelings and let the damage continue.