Luke 9: 59-62 always bothered me. ...He said, "Follow me," But he replied, "Lord, let me go first and bury my father." But He answered him, "Let the dead bury the dead. But you go and proclaim the kingdom of God." And another said, "I will follow you, Lord, but first let me say farewell to my family at home." Jesus said, "No one who sets a hand to the plow and looks to what was left behind is fit for the kingdom of God."
It seems that Jesus doesn't want us to say proper goodbyes to our families, or even perform obligatory necessities, i.e., bury our dead. But it all became clear when I read the Elijah and Elisha story.
1 Kings 19: 19-21
Elijah set out and came upon Elisha, son of Shaphat, as he was plowing with twelve yoke of oxen; he was following the twelfth. Elijah went over to him and threw his cloak over him. Elisha left the oxen, ran after Elijah, and said, "Please, let me kiss my father and mother goodbye, and I will follow you." Elijah answered, "Go back! Have I done anything to you?" Elisha left him and, taking the yoke of oxen, slaughtered them; he used the plowing equipment for fuel to boil their flesh, and gave it to his people to eat. Then Elisha left and followed Elijah as his attendant.
Throwing a cloak over someone evidently meant that you were chosen to follow the prophet. Elisha was willing, so willing that he destroyed his means of making a living. He slaughtered his oxen and had a "goodbye" cookout. The fuel was the equipment Elisha used. Now, Elisha had absolutely nothing to hold him back. He could now follow Elijah.
Jesus wants us to be fully committed.