“And again he entered into Capernaum after some days; and it was noised that he was in the house.”
A few days later, when Jesus again entered Capernaum, the people heard that he had come home — Capernaum has become Jesus' home base, and his return is immediately public knowledge. The word home (oikos) is significant: the house of Simon and Andrew has become the operational center of the Galilean ministry, the place people know to look for Jesus when he returns from the regional circuit. The report that he had come home triggers what verse 2 describes: the immediate gathering of a crowd. The healing of the paralytic that follows happens not in a synagogue or a public square but in a private house — the kingdom breaks into domestic space as readily as religious space.
Church Fathers on Mark 2:1
Because the compassion of God deserts not even carnal persons, He accords to them the grace of His presence, by which even they may be made spiritual. After the desert, the Lord returns into the city.
But Matthew writes this miracle as if it were done in the city of the Lord, whilst Mark places it in Capernaum, which would be more difficult of solution, if Matthew had also named Nazareth. But seeing that Galilee itself might be called the city of the Lord, who can doubt but that the Lord did these things in His own city, since He did them in Capernaum, a city of Galilee; particularly as Capernaum was of such importance in Galilee as to be called its metropolis?
He saw the faith of the sick man himself, since he would not have allowed himself to be carried, unless he’d had faith to be healed.