The Axe Laid to the Root
Old Testament: Isaias 10:33-34
Behold the sovereign Lord of hosts shall break the earthen vessel with terror, and the tall of stature shall be cut down, and the lofty shall be humbled. And the thickets of the forest shall be cut down with iron, and Libanus with its high ones shall fall.
New Testament: Matthew 3:10; Luke 3:9
For now the axe is laid to the root of the trees. Every tree therefore that doth not yield good fruit, shall be cut down, and cast into the fire... For now the axe is laid to the root of the trees. Every tree therefore that bringeth not forth good fruit, shall be cut down and cast into the fire.
The connection
Isaias is describing an army. Assyria has come up against Juda like a forest, and the answer is not a counter army but a woodsman: the tall of stature cut down, the lofty humbled, the thickets felled with iron, Libanus and its high ones brought to the ground. Height is the offence throughout, and iron is the reply. John takes that scene and moves it from nations to persons. The axe is the same and the felling is the same, but what condemns a tree is no longer its height, it is barrenness, and the standard is applied one trunk at a time rather than to a forest. John also moves the axe closer than Isaias had it. Isaias has the Lord coming to fell; John says the axe is already laid to the root, resting against the wood, waiting only for the arm, so that nothing in his sentence is future except the swing. And where Isaias ends with a fallen forest, John adds the fire, so the wood is not merely cut but disposed of, which is the note Christ keeps when He takes up the same words at Matthew 7:19 and carries them to the end of the world at Matthew 13:40.
Moral sense
The tree is not charged with anything. No deed is named against it, only an absence, and the absence is enough. It is possible to be blameless in everything you have done and still be barren.
Anagogical sense
The axe is described as already in position rather than on its way, so the interval before the swing is the whole of the time given, and it is not said to be long.
Warrant
Neither Matthew 3:10 nor Luke 3:9 cites Isaias, and John names no prophet when he speaks. The link rests on the shared scene of judgment as felling, iron laid to timber, with Isaias 10 the nearest Old Testament passage in which the Lord Himself does the cutting. The fire John adds is not in Isaias 10:33-34 (though 10:16-18 burns the same forest), and the pool of fire of Apocalypse 20:15 uses different language again, drawing rather on Sodom and on the pyre of Isaias 30:33, so it is not treated here as the same image continued.
Catechism of the Catholic Church, paragraph 678.