Here there are a couple of incidents which take place on the Sabbath. The Old Testament law taught that a person could not work on Saturdays. As we also saw in Matthew, the Pharisees were the strictest followers of these rules, so they are upset when Jesus and his followers do things on the Sabbath they felt were work. Jesus points out an event from their history where the law was ignored to feed hungry people. Luke then records a similar, or maybe the same, sermon Matthew did. Jesus is teaching that following God requires more than just rule following.
Sometimes people dismiss Jesus’ more extreme teaching by coming up with hypothetical examples in order to dismiss the entire teaching, like when Jesus says to love your enemies. A person says, “Does that mean if someone were to …, I would still need to love them?” That then becomes an excuse for not loving people who have done things far less offensive. It would be good to rethink some of those attitudes of hate, avoidance, revenge, judgment and lack of forgiveness.