When "they" put together the new lectionary (book of Mass readings), the idea was that for Sundays and special liturgical seasons, the first reading (generally from the Old Testament) would have some sort of connection to the Gospel. Ordinarily, the regular daily Mass readings (outside of Advent, Lent and Easter) do not have this; the first reading runs in its own cycle, taking passages more or less in order from the chosen books, which also go more or less in order.
Advent, as I said, is one of the exceptions: the daily Mass readings are as carefully put together as the typical Sunday readings in Ordinary Time (not that homilists are always that clear on just what connection the formulators ever saw between some of the readings!). At any rate, I have really been enjoying the Advent readings and the way they connect, day after day. Until today. Today's readings seem so dissimilar that it would almost seem to be a weekday in good old, unmatched Ordinary Time. About the only connection that immediately comes to mind between the prophecy of Balaam, son of Beor (found in the book of Numbers) and the Gospel for the day is that Jesus is the ultimate fulfilment of Balaam's prophetic message. That's pretty slim pickings for a meditation (never mind a homily!). But I did find a bit of a hint in the Gospel. It's a matter of authority.
In the Gospel, Jesus' preaching is interrupted by a rather rude question: Who gave you the right to teach? Jesus refuses to give an answer, since the questioners were so little interested in real answers that they couldn't answer his challenge: Where did John the Baptist get his right to baptize? (On the grounds that if they said, "From God," they were open to a charge of disbelief and if they said, "From mere human beings," they would cause a riot, the questioners demurred: "We don't know.")
Balaam, Son of Beor, however, doesn't hesitate a bit in saying where he gets his authority. He prefaces his prophetic blessing with this twice-repeated self-identification: "The one who sees what the Most High sees and knows what the Almighty knows." Not that his message was accepted by those who sent for him. They rejected the unwanted message (of Israel's blessing) and the unerring prophet. His authority wasn't the issue in the end.
You have to read the whole story of Balaam (Numbers 22-24, all three chapters). Poor, noble Balaam ended up being considered a false prophet, but he was what he said he was "one whose eye is true, who sees what the Most High sees and knows what the Almighty knows."