I have always believed the Bible is inerrant, but I’m puzzled by the apparent discrepancy between the accounts in Matthew and Luke of the healing of the centurion’s servant: did the centurion meet with Jesus or not?
Inerrancy means the Bible is the inspired Word of God, and is without error. But it doesn’t require each account of an event to be a word for word copy of the others. It helps to remember that even though all 4 Gospels were inspired by the Holy Spirit, each Gospel writer was addressing a different audience and tailored his account of events accordingly. Therefore no single account is necessarily complete in its detail. If you want to know every detail of an event you often have to read all the accounts of that event and piece them together.
The simple explanation in the matter of the Centurion is that Matthew left out the mention of intermediaries whereas Luke included them. But the point of both stories is the same. The Centurion apparently knew that according to the Law Jesus would ceremonially defile Himself by entering the home of a gentile. But his faith was such that he believed if Jesus simply spoke the word, his servant would be healed, and that’s what happened.