While part of this text is found also in Matthew, the latter part (9,60b-62) is exclusive to Luke. It concerns the would-be followers of Jesus, and Jesus’ warnings about what discipleship will entail.
To the first would-be follower who promises to follow Jesus wherever he goes, Jesus responds by stating clearly that unlike even the foxes that at least have holes, he does not have anywhere he can call his own. If the would-be follower is ready for this insecurity, he may follow.
The second person is called to follow by Jesus, but responds by asking for permission to bury his father. This was a duty that was binding on all devout Jews. Jesus’ response is harsh and demands that the disciple be primarily concerned about the kingdom.
The third would-be follower puts conditions to his following namely that he wants to say farewell to his family. However, here too the response of Jesus is clear. Looking back while ploughing leads to a crooked furrow.
While it is not necessary to give up the state of life one has chosen in order to follow Jesus, what is to be understood is that following will necessarily mean changing one’s style of life. It will mean a move from selfishness to selflessness, from acquiring material possessions to sharing them with others and from anything negative to everything that is positive.