When you hear the phrase, 'looking down his nose at them', you know what it means - someone thinks he's better than everyone else! In today's section, it's the religious leaders who were stuck up. They were the Pharisees (a religious sect who prided themselves on keeping God's law) and the teachers of the law (those who studied the laws and prophecies that made up the Jewish scriptures).
Jesus had invited Levi (better known as Matthew) to be one of His followers. But Levi was a tax collector, and tax collectors worked for the Romans - and were known for being dishonest. As outcasts from society, they mixed with other despised people, such as prostitutes.
The religious leaders tackled Jesus on keeping company with such people. They expected Him to behave as they did and only keep company with respectable Jews.
Look at Jesus' reply - "It is not the healthy who need a doctor, but the sick". He wanted the leaders to see that the people they looked down on needed to be forgiven; they needed a Saviour to bring them back to God.
Jesus wasn't saying that the religious leaders were right with God. Later we will see plenty of times when he called them out for being self-righteous: they thought that their efforts at goodness would please God. But they looked down on others and had no love or compassion for those they should have been reaching out to. They thought it was more important to avoid work on the Sabbath (the day of rest) than to show compassion, and tried to make out that Jesus was breaking Sabbath law by healing someone!
The leaders didn't see who Jesus was. They wanted to stick to their rule keeping and religious practices. But Jesus wanted them to see that He was bringing something new - an opportunity to have new life from God, not dead religious self-righteousness. This new life, which God had foretold long before*, could not be patched on to the old religious practices of Judaism (verse 36). The sacrifices and rituals that God had commanded in the past were not His final plan. They were just the clues, pointing forward to the Rescuer who had now come. But the religious experts didn't see it - or didn't want to!