Is 1 Timothy 1:15 a contradiction of what Jesus said in Matthew?

No, 1 Timothy 1:15 is not a contradiction of what Jesus said in Matthew. Paul is not flying in the face of Jesus' words. It is a further revelation and an extension: Christ first came to be King of Israel, but after Israel crucified Him, He came to save sinners.

Les explains that 1 Timothy 1:15 is not a contradiction of what Jesus said in Matthew but a further revelation. Jesus said He came not to destroy but to fulfill. Paul then reveals that Christ Jesus came into the world to save sinners. Les notes that Christ first presented Himself as the King of Israel, doing everything He could to prove He was King, but Israel crucified Him. That did not stop God or interrupt Him; something else was added according to what we have in the Gospels—an extension, not a different message.

1 Timothy 1:15

This is a faithful saying, and worthy of all acceptation, that Christ Jesus came into the world to save sinners; of whom I am chief.

Why did Christ Jesus come into the world according to 1 Timothy 1:15?

According to 1 Timothy 1:15, Christ Jesus came into the world to save sinners, a faithful saying worthy of all acceptance. That purpose did not contradict His presentation as Israel's King; it was a further revelation and extension after Israel rejected and crucified Him.