A summary of the following article from Aquinas:

It is most suitable that the invisible things of Godshould be manifested by visible things. Creatures, as St. Paul says(Rom. 1:20), prove the existence, and show the attributes of God.But the Incarnation, the coming of God himself as man, mostmagnificently shows forth the divine perfections. For God to becomeman is a work of wondrous goodness, wisdom, justice, and power;these "invisible things of God" could not be more noblymanifested than they are in the Incarnation. Now, since goodnesscommunicates itself and spreads itself abroad, it is fitting thatInfinite Goodness should communicate itself in the most perfectmanner, and it does so in the Incarnation. Therefore, it issupremely fitting that God should become man.

Whether it was fitting that God should become incarnate?

Objection 1. It would seem that it was not fitting for God to become incarnate. Since God from all eternity is the very essence of goodness, it was best for Him to be as He had been from all eternity. But from all eternity He had been without flesh. Therefore it was most fitting for Him not to be united to flesh. Therefore it was not fitting for God to become incarnate.

Objection 2. Further, it is not fitting to unite things that are infinitely apart, even as it would not be a fitting union if one were "to paint a figure in which the neck of a horse was joined to the head of a man" [Horace, Ars. Poet., line 1]. But God and flesh are infinitely apart; since God is most simple, and flesh is most composite—especially human flesh. Therefore it was not fitting that God should be united to human flesh.

Objection 3. Further, a body is as distant from the highest spirit as evil is from the highest good. But it was wholly unfitting that God, Who is the highest good, should assume evil. Therefore it was not fitting that the highest uncreated spirit should assume a body.

Objection 4. Further, it is not becoming that He Who surpassed the greatest things should be contained in the least, and He upon Whom rests the care of great things should leave them for lesser things. But God—Who takes care of the whole world—the whole universe of things cannot contain. Therefore it would seem unfitting that "He should be hid under the frail body of a babe in swathing bands, in comparison with Whom the whole universe is accounted as little; and that this Prince should quit His throne for so long, and transfer the government of the whole world to so frail a body," as Volusianus writes to Augustine (Ep. cxxxv).

On the contrary, It would seem most fitting that by visible things the invisible things of God should be made known; for to this end was the whole world made, as is clear from the word of the Apostle (Romans 1:20): "For the invisible things of God . . . are clearly seen, being understood by the things that are made." But, as Damascene says (De Fide Orth. iii, 1), by the mystery of Incarnation are made known at once the goodness, the wisdom, the justice, and the power or might of God—"His goodness, for He did not despise the weakness of His own handiwork; His justice, since, on man's defeat, He caused the tyrant to be overcome by none other than man, and yet He did not snatch men forcibly from death; His wisdom, for He found a suitable discharge for a most heavy debt; His power, or infinite might, for there is nothing greater than for God to become incarnate . . ."

I answer that, To each things, that is befitting which belongs to it by reason of its very nature; thus, to reason befits man, since this belongs to him because he is of a rational nature. But the very nature of God is goodness, as is clear from Dionysius (Div. Nom. i). Hence, what belongs to the essence of goodness befits God. But it belongs to the essence of goodness to communicate itself to others, as is plain from Dionysius (Div. Nom. iv). Hence it belongs to the essence of the highest good to communicate itself in the highest manner to the creature, and this is brought about chiefly by "His so joining created nature to Himself that one Person is made up of these three—the Word, a soul and flesh," as Augustine says (De Trin. xiii). Hence it is manifest that it was fitting that God should become incarnate.

Reply to Objection 1. The mystery of Incarnation was not completed through God being changed in any way from the state in which He had been from eternity, but through His having united Himself to the creature in a new way, or rather through having united it to Himself. But it is fitting that a creature which by nature is mutable, should not always be in one way. And therefore, as the creature began to be, although it had not been before, so likewise, not having been previously united to God in Person, it was afterwards united to Him.

Reply to Objection 2. To be united to God in unity of person was not fitting to human flesh, according to its natural endowments, since it was above its dignity; nevertheless, it was fitting that God, by reason of His infinite goodness, should unite it to Himself for man's salvation.

Reply to Objection 3. Every mode of being wherein any creature whatsoever differs from the Creator has been established by God's wisdom, and is ordained to God's goodness. For God, Who is uncreated, immutable, and incorporeal, produced mutable and corporeal creatures for His own goodness. And so also the evil of punishment was established by God's justice for God's glory. But evil of fault is committed by withdrawing from the art of the Divine wisdom and from the order of the Divine goodness. And therefore it could be fitting to God to assume a nature created, mutable, corporeal, and subject to penalty, but it did not become Him to assume the evil of fault.

Reply to Objection 4. As Augustine replies (Ep. ad Volusian. 137): "The Christian doctrine nowhere holds that God was so joined to human flesh as either to desert or lose, or to transfer and as it were, contract within this frail body, the care of governing the universe. This is the thought of men unable to see anything but corporeal things . . . God is great not in mass, but in might. Hence the greatness of His might feels no straits in narrow surroundings. Nor, if the passing word of a man is heard at once by many, and wholly by each, is it incredible that the abiding Word of God should be everywhere at once?" Hence nothing unfitting arises from God becoming incarnate.