The Jewish religion teaches that only a burnt offering in the temple can earn the forgiveness of sins.
Remember the sign jesus gave about destroying this temple and he will raise it up in three days?
By saying he could forgive sins he was putting himself on par with God, he was also challenging the authority of the priesthood as they were the administers of the old covenant.
Jesus was announcing something theologically new that challenged the social order.
The Jewish leadership should have recognized Jesus as the messiah because there were over 300 prophecies about him, but they were blind to the truth because they loved their power and position more then the promise of the messiah. They assumed the messiah would restore Israel from Roman rule and justify the Jewish priesthood.
They were so blind that even the proof of miracles did not convince them because their hearts were worldly and did not love god. This is a sad commentary on the state of fallen man that even when the miraculous happens men choose not to believe.
This is also a sign of gods disapproval of pride and his pattern of bringing down the proud and raising up the weak and lowly. This is a God who serves and loves.
By first forgiving the man his sin then healing him miraculously he proved he could do the former and revealed his divinity. Jesus was also doing this in the presence of his apostles who were learning what the new covenant was about, and this would serve as a teaching point to them of what Jesus true mission was, to heal the relationship between man and god by the forgiveness of sin. Jesus was likely also exposing his apostles to the outrage and persecution they would endure for following him, but why it was important to do so, and how to handle it.
Each of the gospels also was targeting a particular audience.