Perhaps a role playing argument might fall on deaf ears, but the monk's introduction in the player's handbook (p76)- literally the first sentence-
"Her fists a blur as they deflect an incoming hail of
Now this seems to cast the Deflect Missiles (emphasis on the plural) feature as a more "always on" defense. Considering how the Monk's entire class is built on speed, dexterity, and zen awareness of their environment (in exchange for no armor), it seems pretty reasonable to allow them this constant defensive feature.
Perhaps, if debate is overly heated, a fair compromise would be the Monk can only attack with an intercepted missile once per round. Thus they would maintain reasonable defense while not being overpowered in attack.