Jesus was trying to teach them what He taught many times that the Sabbath was made for the good of the people. It was a time to rest and to do good things. It was not made as a law to hang around the peoples necks that would make life miserable for them. It was a law that the leaders continually bashed and judged others about. However when Jesus posed the questions about whether it was okay to heal on the Sabbath, they could not answer not could they deny they would rescue their son if he was in trouble on the Sabbath thus supporting Jesus teaching that good should be done on the Sabbath.
Jesus then taught on living humbly. He gave a teaching that if one was invited to a banquet it would be wise to sit at the lowest place at the foot of the table rather than to sit at the head of the table. He taught this because if one was to seat himself at the head of the table and the host had invited a person who was more distinguished, that person may be asked to move to a less important seat thus being humiliated. However, if one sat at the foot of the table, the host might see them and move them to a place of greater importance honoring him on front of all the guests. In other words be humble and allow others to honor you rather than be arrogant and be humiliated before others.
Jesus also addressed the role of the host of a banquet by saying the host should not invite his friends, rich neighbors or relatives for they will return the blessing and invite you to one of their events which will be your only reward. Instead, invite the poor, crippled, lame and blind then God will reward you for inviting those who could not repay you. Do good things to those who cannot repay the favor and God will acknowledge the good you have done and will reward you Himself.
Remember, all this time Jesus had been addressing those attending the dinner hosted by the leader of the Pharisees and the type of people he would invite. Most there were sure they would enter the Kingdom of God because of their adherence to the laws, position and their heritage. In fact, one of them commented what a blessing it will be to attend a banquet in the Kingdom of God as if he would surely be there. Jesus took that opportunity to teach them again while making the point that many of them would not attend a banquet in the Kingdom of God. He spoke of a man who prepared a great feast and sent out many invitations. When everything was ready, he sent his servants to tell the invited guests to come for the banquet was now ready. The servants came back and told the host of all the excuses those he had inviting were giving for not attending. One just bought a field and had to inspect it, another bought five pair of oxen and had to try them out and another excused himself by saying he had just been married and could not come because he now had a wife. The host was furious and told the servants to go into the streets and alleys and invite the crippled, lame, blind and poor. These people represented those in the Jewish community thought of as inferior and ceremonially unclean. The servants told the host they had done as he asked and yet there was still room so he sent them into the countryside outside the city to invite even more people. Those in the countryside, far from the city, most likely represented the Gentiles. The host then declared none of those he originally invited but declined would never taste of what he had prepared.
Jesus told them if any wanted to be His disciple they must love Him above their father, mother, wife, children, brothers, sisters and even their own life. If they could not place Him above all others, they could not be His disciple. He also told them if they could not carry their cross and follow Him, they could not be His disciple. (We have looked into this a couple times throughout the NT study regarding carrying your cross. In those times when the Romans crucified anyone, they made that person carry their own cross part of the way to the crucifixion site. This action was a declaration of the prisoner's allegiance and submission to the authority of Rome. Carrying our own crosses in regard to Jesus was to live a life expressing our allegiance to Him and to bend accept His authority over our lives. To be His disciple, one has to submit to Jesus and His authority and pledge our life's allegiance to Him. Without that, a person could not be one of His disciples.)
Jesus concluded the teaching on being His disciple with a bit of a warning. He told them if anyone aspired to be His disciple, he should count the cost before making such a commitment. It would be foolish and humiliating to start the process and end up giving up or quitting on what they promised.