John Chrysostom

This paralytic, however, was different from that one who is set forth in John. For he lay at the pool, but this at Capernaum; and that man had his infirmity thirty and eight years, but concerning this, no such thing is mentioned; and the other was in a state destitute of protectors, but this had some to take care of him, who also took him up, and carried him. …

Homily on the Gospel of Matthew 29 ↗

Jerome

And they brought him, as we said before, a paralytic lying on a bed, because he himself was not able to enter. But Jesus, seeing not the faith of the one who was being offered, but of those who were offering, said to the paralyzed man: Have confidence, my son, your sins are forgiven you. Oh, wonderful humility! He calls despised and weak, dissolved in the joints of all his limbs, his son, whom the priests did not consider worthy of touching. Or certainly he calls him son because his sins are forgiven him. …

Commentary on Matthew ↗

Hilary of Poitiers

Now in the narrative of the paralytic a number of people are brought forward for healing. Jesus' words of healing are worthy of reflection. The paralytic is not told, "Be healed." He is not told, "Rise and walk." But he is told, "Take heart, my son; your sins are forgiven you." The paralytic is a descendent of the original man, Adam. In one person, Christ, all the sins of Adam are forgiven. In this case the person to be healed is brought forward by ministering angels. …

Commentary on Matthew 8.5 ↗

Thomas Aquinas

They brought a paralytic. Here is suggested the devotion of those who brought him; hence in Mark (2:4) it says that because they could not get near him, they let him down through the opened roof. This paralytic signifies the sinner lying in sin; hence, as the paralytic cannot move himself, so neither the sinner. Those who carry him are the ones who by their urgings carry him to God. When Jesus saw their faith, he mentions the favor. …

Commentary on Matthew ↗