Main point summary
The law is not contrary to God's promises because believers - whether Jew or Gentile, slave or free, male or female - are one in Christ by faith, and thereby, are justified in the same way Abraham was.
ὁ οὖν νόμος κατὰ τῶν ἐπαγγελιῶν [τοῦ θεοῦ];
Therefore, is the law contrary to God's promises?
May it never be!
εἰ γὰρ ἐδόθη νόμος ὁ δυνάμενος ζῳοποιῆσαι,
For if a law had been given to give life,
ὄντως ἐκ νόμου ἂν ἦν ἡ δικαιοσύνη•
then truthfully righteousness would be on the basis of the law.
ἀλλὰ συνέκλεισεν ἡ γραφὴ τὰ πάντα ὑπὸ ἁμαρτίαν,
But the Scripture confined everything under sin,
ἵνα ἡ ἐπαγγελία ἐκ πίστεως Ἰησοῦ Χριστοῦ δοθῇ τοῖς πιστεύουσιν.
so that the promise on the basis of Jesus Christ's faithfulness might be given to believers.
Πρὸ τοῦ δὲ ἐλθεῖν τὴν πίστιν
And before the coming of this faith,
ὑπὸ νόμον ἐφρουρούμεθα
we were protected under the law,
συγκλειόμενοι εἰς τὴν μέλλουσαν πίστιν ἀποκαλυφθῆναι,
confined for the faith about to be revealed.
ὥστε ὁ νόμος παιδαγωγὸς ἡμῶν γέγονεν εἰς Χριστόν,
So then, the law became our mentor towards Christ,
ἵνα ἐκ πίστεως δικαιωθῶμεν•
so that we might be justified by faith.
ἐλθούσης δὲ τῆς πίστεως
But since faith came,
οὐκέτι ὑπὸ παιδαγωγόν ἐσμεν.
we are no longer under a mentor,
Πάντες γὰρ υἱοὶ θεοῦ ἐστε διὰ τῆς πίστεως ἐν Χριστῷ Ἰησοῦ•
for all of you are God's sons through faith in Christ Jesus.
ὅσοι γὰρ εἰς Χριστὸν ἐβαπτίσθητε,
For however many of you were baptized into Christ
have been so clothed with Christ.
οὐκ ἔνι Ἰουδαῖος οὐδὲ Ἕλλην,
There is neither Jew nor Gentile;
οὐκ ἔνι δοῦλος οὐδὲ ἐλεύθερος,
there is neither slave nor free;
οὐκ ἔνι ἄρσεν καὶ θῆλυ•
nor is there male and female,
πάντες γὰρ ὑμεῖς εἷς ἐστε ἐν Χριστῷ Ἰησοῦ.
for all of you are one in Christ Jesus.
εἰ δὲ ὑμεῖς Χριστοῦ,
And if you are Christ's,
ἄρα τοῦ Ἀβραὰμ σπέρμα ἐστέ,
then you are Abraham's offspring,
κατʼ ἐπαγγελίαν κληρονόμοι.
heirs according to the promise.
Paul does not draw an absolute contrast between the law and faith, such that the law = bad, while faith = good. The ESV strongly translates φρουρέω and συγκλείω so that it seems to imply such a sharp contrast. But here, the controlling factor in interpretation is that Paul is answering the question, "Is the law contrary to (or antithetical to) God's promises?" He answers in the negative. Therefore, we should find in Paul's argument, not an absolute contrast, but rather the purpose of the law followed by how that purpose is fulfilled. In other words, we ought to expect to find something more nuanced than absolute contrast, the law being clearly inferior but nevertheless serving a good function. Therefore, the law was not a guard that kept us in prison (the "guardian" translation misses the fact that "child" is in the word "παιδαγωγόν," and so connotes some sort of mentor, tutor, trainer, or perhaps nanny who disciplines the child until they grow up). So the distinction between law and faith is less imprisonment vs. freedom, and more immature vs. mature (not to say the imprisonment vs. freedom metaphor is utterly absent). The Scripture, which is to say the Torah, proves to us that we cannot be justified by obedience to the law. But since the Mosaic covenant builds upon the Abrahamic, then gaining the promised inheritance (which includes justification) comes by way, not of a categorically new principle foreign to the covenants, but by way of a principle that predates the even law: faith. Christ is the true promised offspring of Abraham, and thereby, the heir of all of God's promises to Abraham. Since believers are covenantally, mystically, Spiritually united to Christ, then it does not matter whether we are Jewish, Greek, slave, free, male, or female - every believer holds the status of "son" before God the Father. This is totally astonishing considering that, in the Mosaic covenant, free male Jews held a higher status in said covenant than enslaved female Gentiles. The new covenant is no longer mediated through free Jewish men as heads of households, but it is mediated through THE mediator: Christ. Thus, we are all one in him. And since we are one in him, we are all heirs of God's promises to Abraham.