Luke 9:59 And he said unto another, Follow me. But he said, Lord, suffer me first to go and bury my father.
Luke 9:60 Jesus said unto him, Let the dead bury their dead: but go thou and preach the kingdom of God.
This man's father was not dead, but he wanted to stay with his father until he was dead. There is nothing wrong with caring for the father. Jesus earlier made a point of giving to the needs of the parents and seeing that they were cared for.
Mat 15:4 For God commanded, saying, Honour thy father and mother: and, He that curseth father or mother, let him die the death.
Mat 15:5 But ye say, Whosoever shall say to his father or his mother, It is a gift, by whatsoever thou mightest be profited by me;
Mat 15:6 And honour not his father or his mother, he shall be free. Thus have ye made the commandment of God of none effect by your tradition.
They were giving offerings of the money that was to be used for the care of their parents. Another place Jesus says this:
Mat 10:34 Think not that I am come to send peace on earth: I came not to send peace, but a sword.
Mat 10:35 For I am come to set a man at variance against his father, and the daughter against her mother, and the daughter in law against her mother in law.
Mat 10:36 And a man's foes shall be they of his own household.
Mat 10:37 He that loveth father or mother more than me is not worthy of me: and he that loveth son or daughter more than me is not worthy of me.
Mat 10:38 And he that taketh not his cross, and followeth after me, is not worthy of me.
Mat 10:39 He that findeth his life shall lose it: and he that loseth his life for my sake shall find it.
We are to care for the parents and our families, but to follow Jesus we must put his desires first. Let the dead bury their dead: but go thou and preach the kingdom of God. There are brothers who can wait for your father to die. Perhaps like your father they are dead. They are not believers in the Lord Jesus Christ and are spiritually dead. Let the dead bury the dead. We are to put our service to Jesus as a priority. We are not to let excuses keep us from following him. Go thou and preach the gospel of the kingdom of God. Show your new life and start preaching. First preach to your father and family and then go to others. Jesus knew what it meant to serve His father, as he said to his earthly parents:
Luke 2:49 And he said unto them, How is it that ye sought me? wist ye not that I must be about my Father's business?
We serve God by serving others, but they are not to control us. Jesus is Lord, we serve him; so we must preach the gospel. Jesus is Lord and master of our lives.