Again....context is everything in understanding the Word.
In this passage we see it is Jesus who forgives the sin....not the disciples.
From Matthew 9:1-8 (NASB)
1Getting into a boat, Jesus crossed over the sea and came to His own city.
2And they brought to Him a paralytic lying on a bed. Seeing their faith, Jesus said to the paralytic, “Take courage, son; your sins are forgiven.”
3And some of the scribes said to themselves, “This fellow blasphemes.”
4And Jesus knowing their thoughts said, “Why are you thinking evil in your hearts?
5“Which is easier, to say, ‘Your sins are forgiven,’ or to say, ‘Get up, and walk’?
6“But so that you may know that the Son of Man has authority on earth to forgive sins”—then He said to the paralytic, “Get up, pick up your bed and go home.”
7And he got up and went home.
8But when the crowds saw this, they were awestruck, and glorified God, who had given such authority to men.
He gave the power to forgive sins to the disciples after the resurrection; see John 20:23.