Why was John exiled to the island of Patmos?

John himself explains why he was on Patmos in Revelation 1:9, where he calls himself a companion in tribulation and says he was on the isle "for the word of God, and for the testimony of Jesus Christ." This shows that his presence there was tied directly to his faithful preaching and witness of Christ, not to any wrongdoing on his part.

John was one of the apostles God used to establish the church, and in that work he experienced much persecution and trials that developed patience in him. He was waiting for the return of the Saviour and had a joyful expectation of being with the Lord. It was in the midst of this tribulation, brought on by his testimony of Jesus, that the Lord called him to Patmos.

While he was there, the Lord used the setting to enlighten John about the things that would come to pass before the coming of the Lord. So his exile, rooted in his faithful witness for Christ, became the very occasion through which he received the revelation meant to warn and comfort the whole body of Christ.