Gibbs, Jeffrey A. “Matthew 8:5-13: Jesus Heals a Centurion's Servant." Matthew 1:1-11:1. St. Louis: Concordia Publishing House, 2006, pp. 414-420.
Gibbs notes that the centurion, possibly not a Roman, as Syrians and Idumaeans were active in the Roman forces, shows Jesus honor and begs his assistance (Gibbs 2006, 414). Jesus' response suggest sstrongly that the centurion is not an Israelite, as he is compared to what Jesus had seen "in Israel." Gibbs sees this as parallel to Luke 7, and not contradictory, though in Luke Jesus is approached by Jewish representatives. The request still comes from the centurion (Gibbs 2006, 415). In additional defense of the event being the same, while Luke mentions a servant, Matthew uses the word παῖς, which only rarely refers to a son in the New Testament. Gibbs takes the sick person to be a servant.
The centurion's response to Jesus' offer of a personal visit both emphasizes that the centurion is not worthy. Gibbs observes the very emphatic word order used. Further, though the centurion does not imply that Jesus is under authority, he says clearly that he himself is (Gibbs 2006, 416).
Gibbs notes that in the initial encounter, the centurion does not actually ask Jesus to do antyhing. He merely states the problem. It is Jesus who suggests the solution (Gibbs 2006, 417). The narrative then becomes not so much about the need of the servant but about the conversation pertaining to Jesus' authority to heal. Jesus rather surprisingly states his willingness to enter the home of a Gentile and heal a servant. The centurion shows his own humility by acknowledging Jesus' authority (Gibbs 2006, 418). Jesus' authority extends beyond that of any earthly ruler, since he can command an illness to go away.
Jesus' response of praise and wonder is surprising to Gibbs. He speaks not to the centuryon but to those following him, praising the centurion's faith (Gibbs 2006, 418). In his praise, he also predicts that those of all nations will be brought together into the heavenly gathering. God gathers all nations, like that of the centurion (Gibbs 2006, 419).
Gibbs finally notes the word of caution which Jesus brings to the crowds. They must also trust Jesus' authority so as to be gathered into the kingdom (Gibbs 2006, 419). It is Jesus' authority which makes all things possible, including the healing of the centurion's servant. Gibbs lists a number of other New Testament passages which speak of God's welcome of all who believe in Jesus.