I don't think they misunderstood him.
Only God can forgive sin.
Jesus, also,
was permitted to do so (and still does it, as Lord).
Mat 9:6 But that
you may know that the Son of Man has authority on earth to forgive sins"—he then said to the paralytic—"Rise, pick up your bed and go home."
Mark 2:7 "Why does this man speak like that? He is blaspheming! Who can forgive sins but God alone?" (Read there)
Mar 2:10 But that you may know that
the Son of Man has authority on earth to forgive sins"—he said to the paralytic—
Mar 2:11 "I say to you, rise, pick up your bed, and go home."
Mar 2:12 And he rose and immediately picked up his bed and went out before them all, so that they were all amazed and glorified God, saying, "We never saw anything like this!"
Luk 5:21 And the scribes and the Pharisees began to question, saying, "Who is this who speaks blasphemies? Who can forgive sins but God alone?"
Luk 5:24 But that you may know that
the Son of Man has authority on earth to forgive sins"—he said to the man who was paralyzed—"I say to you, rise, pick up your bed and go home."