St. Thomas on Justification - The Purpose of the Incarnation

The Incarnation was for the sake of taking away sin.

It is certain that Christ came into this world not only to take away that sin which is handed on originally to posterity, but also in order to take away all sins subsequently added to it... ST III, Q1, A4

One obvious inference that we may draw from this is that we cannot be saved apart from Christ: if there was no Incarnation, we would have no Savior; consequently we would still stand condemned by our sins.

The Word became flesh for us in order to save us by reconciling us with God, who "loved us and sent his Son to be the expiation for our sins": "the Father has sent his Son as the Saviour of the world", and "he was revealed to take away sins":

Sick, our nature demanded to be healed; fallen, to be raised up; dead, to rise again. We had lost the possession of the good; it was necessary for it to be given back to us. Closed in the darkness, it was necessary to bring us the light; captives, we awaited a Saviour; prisoners, help; slaves, a liberator. Are these things minor or insignificant? Did they not move God to descend to human nature and visit it, since humanity was in so miserable and unhappy a state? [CCC §457; cf. 1Jn 4:10, 14; 3:5]

A second inference is that if we cannot be saved apart from Christ, then no deeds of our own can obtain for us forgiveness for our mortal sins. Because our mortal sin involves turning away from the infinite, immutable good - namely, God (cf. ST I-II, Q87, A4) - reparation for it is beyond our finite abilities.

No one can merit for himself restoration after a future fall, either condignly or congruously. He cannot merit for himself condignly, since the reason of this merit depends on the motion of Divine grace, and this motion is interrupted by the subsequent sin; hence all benefits which he afterwards obtains from God, whereby he is restored, do not fall under merit--the motion of the preceding grace not extending to them. Again, congruous merit, whereby one merits the first grace for another, is prevented from having its effect on account of the impediment of sin in the one for whom it is merited. Much more, therefore, is the efficacy of such merit impeded by the obstacle which is in him who merits, and in him for whom it is merited; for both these are in the same person. And therefore a man can nowise merit for himself restoration after a fall. [ST I-II, Q114, A7; emphasis added]

Thus we cannot hope to merit forgiveness for mortal sin by anything that we do, but can only hope to obtain forgiveness through the merits of Christ's work of atonement. Consequently the Incarnation is necessary for our salvation if we are to be saved at all, because we cannot save ourselves. Hence we see in the purpose of the Incarnation itself that they are badly mistaken who suppose that the Catholic Church teaches we may save ourselves by our works.