The etymology of "excuse" is:
"attempt to clear (someone) from blame"
also:
"pardon"
ex (meaning out or away)
causa (meaning accusation or justification for action)
The etymology of forgive is to "grant or pardon". Something that cannot be done solo.
I disagree that forgiveness (of people that aren't sorry) is essential for a better life. Better than what? Is my life so horrible because I won't forgive my mother in law for removing the dog? I have no emotions regarding the issue.
If pretending that forgiveness took place helps you process your emotions, and get them out, then it's healthy, but it's not forgiveness. If it's just a way to ignore your anger, it will kill you.