What does Luke 11:38 mean?
A Pharisee has invited Jesus to his home for a formal banquet (Luke 11:37). Pharisees follow the Mosaic law but add an extra-biblical Oral Law. These traditions include specific instructions about daily life, such as ceremonially washing hands. They are so meticulous that they wash after leaving the marketplace, and wash eating implements even if they are not unclean (Mark 7:3–4; Leviticus 11:32–33).We don't know how many times Jesus dines with Pharisees throughout His ministry, but Luke mentions three; in each event Jesus manages to offend His host.
At the first meal, Jesus allows a woman with an immoral reputation to clean His feet with her hair and tears; the Pharisee thinks that if Jesus is such a great prophet, He would know what kind of woman she is and be disgusted with her touch. Jesus corrects the Pharisee and explains she acts so because she knows she is loved and forgiven (Luke 7:36–50).
In this event, Jesus doesn't wash His hands. This doesn't refer to the courtesy of providing water to wash away the dirt and grime of the road. It's strictly ceremonial and not required in the Mosaic law.
In the third event, a Pharisee invites Jesus on the Sabbath. While there, Jesus heals a man. Jesus explains to the Pharisees and lawyers that if they would pull their ox out of a well on the Sabbath, why shouldn't He heal a man? They have no response but to despise Him more (Luke 14:1–6).