What the Bible says
“Then Peter took him, and began to rebuke him, saying, Be it far from thee, Lord: this shall not be unto thee.”
Matthew 16:22 (KJV)
“Get thee behind me, Satan: thou art an offence unto me: for thou savourest not the things that be of God, but those that be of men.”
Matthew 16:23 (KJV)
“Get thee hence, Satan: for it is written, Thou shalt worship the Lord thy God, and him only shalt thou serve.”
Matthew 4:10 (KJV)
From rock to stumbling stone
Only a few verses earlier Peter confessed that Jesus is the Christ, and Jesus called him blessed. Then Jesus began to explain that he must suffer, be killed and be raised the third day. Peter took him aside and rebuked him. The disciple who had just been called a rock had become a stumbling stone in the road to the cross.
The same temptation again
In the wilderness Satan offered Jesus the kingdoms of the world without the cross, and Jesus answered, 'Get thee hence, Satan.' Peter, out of love and fear, was offering the same shortcut. Jesus recognised the voice behind the words.
Rebuke is not rejection
Jesus did not send Peter away. He kept teaching him, took him up the mountain of the transfiguration days later, and after Peter's three denials came looking for him by the sea (John 21). Sometimes love has to say no to what we want for the people we love — and Jesus's no was the way to our salvation.
Common questions
Did Jesus think Peter was possessed?
No. 'Satan' means adversary. Jesus was rebuking the temptation in Peter's words — avoiding the cross — which echoed the devil's temptation in Matthew 4.
Did Jesus forgive Peter?
Yes. Peter remained a leading apostle, and after his denials Jesus restored him three times by the Sea of Galilee (John 21:15–17).