What does Luke 13:22 mean?
Luke reminds us that Jesus is traveling toward Jerusalem. The "travelogue" (9:51—19:27) is a series of stories recounting how Jesus prepared the disciples for His death and resurrection and their work establishing the church. Jesus trains them to spread the kingdom of God like a growing mustard seed or leaven (Luke 13:18–21) while He walks toward Jerusalem to do the work that will ensure the fulfillment of God's kingdom on earth: the crucifixion and resurrection.The reminder of Jerusalem also serves to highlight the irony of the events of the section. Jerusalem is the epicenter of Jewish religion and religious leaders. So far, those leaders have favored manmade laws over the wellbeing of fellow Jews (Luke 13:10–17). Those who should know best will miss the fulfillment of God's kingdom because they reject His Son (Luke 13:25–35).
Luke isn't implying that Jesus was traveling alone in this passage. Most stories in the "travelogue" are not found in the gospel of Mark. Many are not found in Matthew. Luke carefully chose parables and miracles to build Theophilus's faith (Luke 1:1–4). Although this section begins with Jesus healing a Jewish woman (Luke 13:10–17) and ends with Jesus lamenting that Jews will reject Him (Luke 13:31–35), the parables of the mustard tree and leaven show how God's kingdom will spread throughout the entire world and bring rest for Gentiles (Luke 13:18–21). Now, Jesus shows that many Gentiles will enter the narrow door before Jews do (Luke 13:29–30).