If a man of God anoints someone and the person is healed, it's not the minister who healed the person; he was just God's instrument.
Every Christian understands this.
But many non-Catholics cannot comprehend the idea of receiving forgiveness of sins from a priest.
They CAN believe in restoring sight, cleansing leprosy, or raising the dead at the hands of a minister -- but NO WAY the invisible forgiveness of sin (because only God can do that!).
Yet it was the resurrected Jesus who delegated his apostles with this authority:
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Jesus said to them again, “Peace be with you. As the Father has sent me, even so I send you.” And when he had said this, he breathed on them, and said to them, “Receive the Holy Spirit. If you forgive the sins of any, they are forgiven; if you retain the sins of any, they are retained.” (John 20:21-23)