Peter objected. In essence, Jesus told Peter that He needed to be willing to accept the service of Jesus and others. It is humbling to be served by others, especially your superiors. However, by rejecting their service, we assert our stubborn independence and claim that we have no need of their service to us.
This is obviously true of Jesus. We need his ministry. We cannot live without it. It is also true of our brothers and sisters in Christ. They are in Christ's place ministering to us. We cannot refuse their service in the name Jesus.
If you do not receive Jesus' ministry and cleansing, you have no part in HIm. The same is true of those sent by Jesus to minister to us.