The apostles argued on the road about the possibility of who would lead the group to fill in the vacuum in case the predictions Jesus made actually happened. They heard Jesus twice foretold that he was going to be rejected by the Chief priests and the Scribes and be killed and three days later he would rise again. The predictions sparked the dispute amongst themselves about the possibility of the future leadership. The positive aspect of the discussion showed that they had no plan to disperse themselves after the arrest of Jesus. They were in hiding and lived in fear but not disband. The negative outcome was the disunity of the group and the lack of faith in Jesus.
We could have done no different. We would have talked about plans for the group or if we wanted the group to exist after Jesus had gone. The group must have a leader especially in a hard time that was ahead to keep the group going. Without a good leader the group ceases to exist. What went wrong for the apostles was not about the future leadership discussion but was more about the superiority. The question of finding the best candidate for the job was the main topic of the discussion. In the pass when they didn't understand what Jesus taught in public they would ask Him in private for an explanation. This time they went alone by themselves, consulted not Jesus but relied on their own worldly wisdom rather God's.
Fighting for the leadership role is a form of selfish ambition in disguise. It is opposite to Christian humility. It is a desire to lead, to dominate rather than a desire to serve. It is a thirst to satisfy one's needs rather than serving the needs of others. It is a hunger for power and fame and control. St James 3,16 said something like envy and selfish ambition opens the door to welcome disorder and wickedness. Selfish ambition causes quarrels and fights within the apostles' community. They failed to ask Jesus, who was walking ahead of them on the same road, for direction and guidance but took the matter into their own hands. They left Jesus aside and acted as if Jesus wasn't their leader any more and they needed a replacement.
Individual selfish ambition often obstructs success rather than promotes it and a group ambition creates disunity and factions within a group. In a corporate world the higher one's position in an organization, the more that person depends on others for success. When a person has a reputation to put down others for his own ambition, how can he expect others to trust and follow his leadership. Helping a self ambitious person to the top job is harmful for everyone because that person would put his ambition above the life of others while investing in the lives of other people is a right and noble thing to do. When the leadership role is unstable that leader has time for nothing else apart from try to consolidate his job.