I understand that it is impossible for a non-Christian to understand the concept of true forgiveness toward another person. Is that correct?
Most spiritual concepts are difficult for non-believers to grasp. Not because the concepts are hard, but because it requires looking at the world from a framework that makes non-believers uncomfortable.
"These things we also speak, not in words which man's wisdom teaches but which the Holy Spirit teaches, comparing spiritual things with spiritual. But the natural man does not receive the things of the Spirit of God, for they are foolishness to him; nor can he know them, because they are spiritually discerned. But he who is spiritual judges all things, yet he himself is rightly judged by no one. For "who has known the mind of the LORD that he may instruct Him?" But we have the mind of Christ" (I Corinthians 2:13-16).
"For the message of the cross is foolishness to those who are perishing, but to us who are being saved it is the power of God.
"For it is written: "I will destroy the wisdom of the wise, And bring to nothing the understanding of the prudent." Where is the wise? Where is the scribe? Where is the disputer of this age? Has not God made foolish the wisdom of this world? For since, in the wisdom of God, the world through wisdom did not know God, it pleased God through the foolishness of the message preached to save those who believe. For Jews request a sign, and Greeks seek after wisdom; but we preach Christ crucified, to the Jews a stumbling block and to the Greeks foolishness, but to those who are called, both Jews and Greeks, Christ the power of God and the wisdom of God. Because the foolishness of God is wiser than men, and the weakness of God is stronger than men.
"For you see your calling, brethren, that not many wise according to the flesh, not many mighty, not many noble, are called. But God has chosen the foolish things of the world to put to shame the wise, and God has chosen the weak things of the world to put to shame the things which are mighty; and the base things of the world and the things which are despised God has chosen, and the things which are not, to bring to nothing the things that are, that no flesh should glory in His presence" (I Corinthians 1:18-29).
In a sense, non-believers don't understand because it is too simple, too straight forward. But the power of the Word is in its simple message. It is not impossible to understand, it is just hard to accept and keep a worldly viewpoint at the same time.