Bottom line: Identification with the gospel's purpose brings a demonstration of the gospel's power.
Paul confronted Peter in Galatians 2 because Peter was not living in accordance to the truth of gospel. He wasn't living out his identity with the gospel. When we find our identity in anything other than the gospel, then we lose out on the power available to us through Jesus and His good news. But, when we live out our identity with the gospel, then the life of Jesus is demonstrated through us. This demonstration of Jesus' life is a mighty witness to those who are lost.