The great exchange means you are dealing with Jesus in that Christian who sinned against you.

So if you consider me your partner, receive him as you would receive me. If he has wronged you at all, or owes you anything, charge that to my account. I, Paul, write this with my own hand: I will repay it—to say nothing of your owing me even your own self.

So writes Paul to Philemon about his runaway slave, Onesimus.

Notice the exchange that takes place.

First, Paul says that Onesimus is being sent back to Philemon as Paul’s representative. Philemon must regard this slave who has sinned against him as Paul.

Second, Paul says that Onesimus’ sin against Philemon must be held against Paul.

Get that? Paul became Onesimus’ sin so that Onesimus could become Paul’s righteousness — his standing before Philemon.

Is that not the Great Exchange? According to Paul’s second letter to the Corinthians, we get Christ’s mission as the personification of the righteousness and faithfulness of God because Christ took our sin (Paul is speaking of Apostles here but I’m sure he would agree that the principle applies more widely):

Therefore, we are ambassadors for Christ, God making his appeal through us. We implore you on behalf of Christ, be reconciled to God. For our sake he made him to be sin who knew no sin, so that in him we might become the righteousness of God.

Onesimus the slave who sinned is, to Philemon, now an ambassador from Paul.

And this brings us to the sticking point.

Every Christian you know is sent to you by Jesus. Each one was commissioned in baptism to be Christ’s representative. And this calling is not destroyed by the ways they have sinned against you, much less annoy you.

You are supposed to receive them as you would receive Jesus. And any wrong they have done you, you are to charge to Christ’s account. He will repay it — to say nothing of your owing Him your very self.