Balaam saw not the angel because God withheld his eyes, as he did the eyes of Daniel's companions, Daniel 10:7. It is a truth, which mere philosophers own, that when God withdraws his concourse or help from any of his creatures, they cannot perform their natural acts and offices; the eye cannot see, as Ge 19, nor the ear hear, nor the fire burn, as Da 3.
Related Commentaries of Numbers 22:23
Numbers 22:23
23 And the ass saw the angel of the LORD standing in the way, and his sword drawn in his hand: and the ass turned aside out of the way, and went into the field: and Balaam smote the ass, to turn her into the way.