In Luke 13, Jesus is seen as caring very much for spiritual truth. He wants His followers to get their theology right.
For instance, what about our understanding of suffering? It's a natural tendency to believe that bad things happen to bad people. I visited someone recently who questioned if his health problems are the result of a judgment. While that possibility should always be prayerfully considered, I seriously doubted it to be the case in his situation. Instead, I pointed out that suffering is an equal opportunity affliction. In fact, Job suffered not because he was guilty, but because he was righteous!
It was the same with Jesus. Jesus also drew the crowd's attention to some tragedies of his day. People crushed by a falling tower - were these 18 worse sinners than anyone else? The Galileans killed by Pilate - were they more guilty than their neighbors? Jesus said "no" on both counts. Still, the lesson we should draw from them is repentance. Judgment is coming, and we need to get right with the Lord.
Jesus is also concerned that we get our understanding of Sabbath and Christian freedom right. Should healing be withheld until after the Sabbath? Jesus was moved to release a woman from her infirmity at the synagogue service. She had been bound for 18 long years - why make her wait one additionally day? Isn't the Sabbath supposed to be a day for celebration, for joy, for life, for healing? The Pharisees didn't think so. They got it wrong.
The problem is, we often don't get it right, either. Jesus was asked in vs. 23 if only a few people are going to be saved. Sadly, the apparent answer is yes. Most people, Jesus said, will wait until it is too late to try to enter the kingdom of heaven. They won't be motivated until the door is shut - and then it will be too late.
Be sure to get this right: Don't put off getting right with the Lord!