3 Cor 4:12-18 states (my trans.):
12 But God, the almighty, because he is righteous and he did not want to annihilate his own creation, 13 caused the Spirit through fire to descend into Mary the Galilean, 15 so that, by this same pershing flesh, by which the Evil One exercised his reign, he was defeated and convinced that he was not God. 16 For Christ Jesus saved all flesh by his own body, 17 so as to consecrate a temple of righteousness in his own body, 18 by which we have been liberated.
Beginning in 4:12, 3 Cor starts to detail how God initiated his plan of salvation for humanity. At this point, the logic of the text begins to look like a significant passage in another Pauline letter: Romans 3:19-22. There, Paul says:
Now we know that whatever the law says it speaks to those who are under the law, so that every mouth may be stopped, and the whole world may be held accountable to God. For by works of the law no human being will be justified in his sight, since through the law comes knowledge of sin. But now the righteousness of God has been manifested apart from the law, although the Law and the Prophets bear witness to it– the righteousness of God through faith in Jesus Christ for all who believe.
In 3 Cor, the problem that needs to be solved is that the creation was in danger of annihiliation by God (which God did not wish to do). Similarly, in Romans 3 the major problem is that every person is found guilty before God. The solution, on the other hand, is δικαιοσύνη θεοῦ, which is through the πίστεως Ἰησοῦ Χριστοῦ for all who believe. These two phrases, δικαιοσύνη θεοῦ and πίστεως Ἰησοῦ Χριστοῦ, have themselves become centers of controversy in Pauline scholarship. Scholars dispute whether δικαιοσύνη θεοῦ refers to something God grants to believers or else an aspect of his character, over which scholars likewise debate. As for the phrase, πίστεως Ἰησοῦ Χριστοῦ, the dispute circles around whether it is “faith in Christ” or “the faith/faithfulness of Christ”. One scholar who represents the New Perspective on Paul, N.T. Wright, argues for an interpretation of Romans (e.g., Romans, NIB 10, ad loc.) which seems to be confirmed by 3 Cor 4:12-18 here. His position is that the righteousness of God is God’s own faithfulness to his covenants, which included promises to save Israel and the world, and that πίστεως Ἰησοῦ Χριστοῦ is Christ’s own faithfulness, the ministry and death resurrection by which God has kept his promises. 3 Cor 4:12-14 closely parallels Wright’s interpretation of that epistle. That is, here, it is because God is righteous that he sends the Spirit to Mary in order to bring Jesus into the world in flesh, and it is in that flesh that Christ saves all flesh. God’s righteousness mentioned in 4:12 provides a motive for him to save the world, not destroy it. If one asks how God’s righteousness could provide a motive for him to save the world, the simplest answer seems to be along the lines that Wright suggests for Romans: to be righteous, God must keep his promises, or else he would be a liar, because God promised to save the world in his covenants. Thus to be righteous, he must become the world’s saviour.