Why did the centurion in Capernaum believe that only a word from Jesus would be sufficient to heal his servant?
There are two views of why the centurion in Capernaum believed that only a word from Jesus would be sufficient to heal his servant:
The centurion acknowledges Jesus’ power shown in his ability to heal with merely a word.
The centurion actually sees Jesus as his Redeemer, unlike the initial attitude of another official from Capernaum (John 4:49), and so trusts in his willingness and power to help his son.
Interpretation 1:
Since the text of Matthew 8:8 contrasts the phrase come under my roof
with only say the word,
it is likely that what the centurion had in mind here is a word of a reassurance such as your servant will recover,
or perhaps a word of advice such as do this and then your servant will recover.
Jesus can merely give the command and it is not necessary for him to come in person, for that would be inappropriate for the Lord. The servant of the centurion himself can merely carry out Jesus’ instructions. If Jesus simply speaks the word, everything will turn out all right and the servant who was attacked will be healed.1
Interpretation 2:
The fact that the centurion looks towards Jesus for help in desperation also reveals that he indeed views him as his Redeemer. His faith is revealed in the fact that he confesses to believe that Jesus can do spectacular miracles (which stands in sharp contradistinction with another official in Capernaum in John 4:49). Jesus is of course able to heal in the way he sees fit, even by simply speaking the word from a distance.2
8 Le centenier répondit: Seigneur, je ne suis pas digne que tu entres sous mon toit; mais dis seulement un mot, et mon serviteur sera guéri.