Verse 20: Now a mediator is not a mediator of one, but God is one. In other words, there are two parties required for a mediation. In this case, Moses and the nation of Israel. In context, I believe that the verse is pointing out the difference between the giving of the law which required Moses as the mediator and the giving of the covenant which God mediated on His own with Abraham.
Verse 21: Is the law then against the promises of God? God forbid: for if there had been a law given which could have given life, verily righteousness should have been by the law. The question is, does the law set aside the promises of God that he gave to Abraham in the covenant? No. They actually run parallel. One does not trump the other. However, the law could not give life, for if it could, it would have replaced the promises, i.e., those made to Abraham 430 years prior.
Verse 22: But the scripture hath concluded all under sin, that the promise by faith of Jesus Christ might be given to them that believe. Instead, the scripture, i.e., law, has made it abundantly clear that all are under sin, both Jew and Gentile. Notice also that the faith was first that of Christ, and we merely believe in that faith with our own.
Verse 23: But before faith came, we were kept under the law, shut up unto the faith which should afterwards be revealed. In other words, the purpose of the law was to keep the nation shut up unto the faith which should afterwards be revealed in and through Christ. The term shut up unto the faith can also be translated imprisoned or confined. In other words, they were controlled or under the law until Christ came because his was the faith that made it possible. Anyone who teaches that everyone has always been saved by grace through faith is confused because the nation of Israel was incapable of this kind of faith because it had been shut up unto them until Christ came.
Verse 24: Wherefore the law was our schoolmaster to bring us unto Christ, that we might be justified by faith. The law served as the nation's schoolmaster which was given to point them to Christ so that they might be justified by faith.
This is one of the most misunderstood verses in all of the Bible, because we fail to recognize that the pronouns our and we are referring to the nation of Israel and not the Body of Christ. The Body of Christ has never been kept under the law (cf. verse 23). The law was given to the nation to bring them to Christ, so that they could be justified by faith.
Verse 25: But after that faith is come, we are no longer under a schoolmaster. The faith that was to come was through Christ, and the law is no longer their schoolmaster. Again, the law pointed them to Christ. Obviously, the faith was not prior to Christ!
Verses 26-27: For ye are all the children of God by faith in Christ Jesus. For as many of you as have been baptized into Christ have put on Christ. Note the change in pronouns, i.e., ye. He changes from the first-person plural to the second-person plural. Paul is now referring to the Galatians which were both Jew and Gentile. All of them must come by faith in Christ and not the law. By their faith, they had been baptized into Christ and had put on Christ apart from the law. This baptism has nothing to do with water.
Verse 28: There is neither Jew nor Greek, there is neither bond nor free, there is neither male nor female: for ye are all one in Christ Jesus. Under the law there was Jew and Greek, bond and free, male and female, but not now! How can you not be a dispensationalist after reading a verse like this!?