It would be like accepting defeat in their eyes. The ultimate in humiliation. Or so they thought. Jesus had given them time to act as they should. As much as Peter enjoyed public praise from Jesus, he missed a golden opportunity by not getting on his knees and doing the work of a servant.
Pride can cause one to miss many golden opportunities.
Jesus was hurt by this show of pride from His closest friends. All His teachings and examples seemed a total waste upon those who followed Him closely. What could He do at this last meal with them to help them understand His mission and the way they were to think and act. Jesus quietly took off his garment, wrapped a towel around Him in the form of a servant, got down on the floor at the feet of His friends and began to wash them. This action opened the eyes of the disciples.