Jesus climbed into a boat and went back across the lake to his own town. Some people brought to him a paralyzed man on a mat. Seeing their faith, Jesus said to the paralyzed man, “Be encouraged, my child! Your sins are forgiven.”
But some of the teachers of religious law said to themselves, “That’s blasphemy! Does he think he’s God?”
Jesus knew what they were thinking, so he asked them, “Why do you have such evil thoughts in your hearts? Is it easier to say ‘Your sins are forgiven,’ or ‘Stand up and walk’? So I will prove to you that the Son of Man has the authority on earth to forgive sins.” Then Jesus turned to the paralyzed man and said, “Stand up, pick up your mat, and go home!”
And the man jumped up and went home! Fear swept through the crowd as they saw this happen. And they praised God for sending a man with such great authority. http://bible.us/Matt9.1.NLT

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"Does he think he’s God?”

Who can say that sins are forgiven? Well everyone knows the answer to that question. Only God can forgive sins.
Jesus had been healing people and I might add for free. Seems like a really nice guy. Word is getting around that Jesus has been spending time with the down and outers. He's been healing the sick for nothing in return, he's been feeding hungry people. He sounds like a nice guy. Actually most people are saying he's a good man, a honest teacher,  maybe even a prophet of God.

But this is too far! Good people don't go around claiming to be God. Obviously that would be a lie and lying is not good.

Isn't that just the way it is, God gives someone a little power and it goes to their head. Surely Jesus hasn't went off the rails.

I'd have not have believed it if I'd not had heard it with my own ears. Jesus is not only making a claim to be God, he's saying that his healing and miracles are a proof that his words are true. So I'm left with this question, does Jesus have the right,  the authority, the proof to say he's God?

That's what he's putting before us all. If Jesus is God then, well, we better be listening and understanding. If he had the power and authority to forgive sins, I better get in the queue. Everyone knows healing may help in this life but the real deal clincher is the life to come. And everyone also knows that sins are the big barrier.

A little later in Matthew's gospel,  the same questioners ask why Jesus hangs out with scum, why is he rubbing shoulders with lowlife, why sully himself with sinners?

Jesus answers that sick people need a doctor.

So it is obvious, "Does he think he’s God?”

Yes, he does. He is claiming to have the authority to heal sinners. He is a sin healer. A sin doctor.  Jesus is God.