Older Bible scholars disagreed about this too — here’s each side, in their own words.
Public-domain commentators, 1600s–1900s, in their own words — voices on both sides.
Read as a real contradiction
Read as reconcilable
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Consequently it is nothing out of the way for Matthew … when thus dealing with an approach on the part of the centurion to the Lord, which was effected in the person of others, to have chosen to express the matter in this compendious method, There came a centurion to Him.
Augustine (d. 430), The Harmony of the Gospels II.xx (NPNF transl., 1888).
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Those who think that Matthew and Luke give different narratives, are led into a mistake by a mere trifle … there is no impropriety in Matthew saying, that the centurion did what was done in his name and at his request.
John Calvin (d. 1564), Commentary on a Harmony of the Evangelists, on Matthew 8:5.
In the commentators’ own words