What does Matthew 8:7 mean?

A Roman centurion has approached Jesus with a message that one of his servants is paralyzed and suffering. He is near death. We know from Luke's report on this incident (Luke 7:1–10) that the centurion had great respect for the Jewish people and their customs. He had clearly heard about Jesus and all the remarkable healings He had done in the region.

Jesus does not hesitate. He says He will come and heal the servant. Some translations take the Greek phrasing here as a question where Jesus asks if He should come and heal the servant. Luke tells us that Jesus set out in the direction of the centurion's house.

Once again, Jesus seems willing to break from Jewish cultural conventions. Jewish people in that era had extended commands not to participate in certain activities with Gentiles. That even included not ever entering a Gentile person's home. Jesus seems unconcerned with following this standard. Out of respect for Jesus, and in personal humility, it seems the Roman centurion had no intention of asking such a thing of Christ (Matthew 8:8).