Basic Principles of the Paragraph Containing Gal 3.
1, the every day example. Back in 14 he made a purposive statement that he believed needed to be explained. it was:
Christ did this in order that the blessing God promised to Abraham might be given to the Gentiles, so that we might recieve the promise of the Spirit --which is how the mission gets done.
"This" was the death on the cross.
Now the every day example comes about the Promise. When two men agree and sign off on the agreement, the terms have to be met. The "two men" are God and Christ. How does Christ get the gift of the Spirit to give to men to further spread the mission of the Gospel? Through his agreement with God. The so-called Abrahamic covenant was actually between God and Christ the Seed. The agreement was not with Many but with One person.
2, The Seed. With Israel as an ethne out of the picture in the agreement, Paul was showing that the Promise was (indirectly) for all mankind, for all nations, because it was not for one nation. It was a matter of clearing up who the "two men" were.
3, V 17 then opens with 'touto de lego' because he knows it is going to be remarkable that Israel was not the other party of the covenant often called the covenant with Abraham. But it is fundamental. This is why the Gospel blesses all people no matter what ethne they are . He knows he needs to re-express, or re-phrase this fundamental assertion, so here it comes:
The Law cannot break that agreement and void God's promise to Christ
Who cares? JUDAISM cares! That's what Paul grew up in, grew out of, and now battles. Judaism now says that the covenant was with Many and that many was Israel. So Law in these next verses (18, 19) means people fulfilling the terms of Moses law as though they were the other party in the agreement--WHICH THEY ARE NOT! Christ was the other party. (He has no concern here to point out that Christ fulfilled the Law as in Rom 10:4).
18b is showing that it couldn't have been Abraham's obedience to law, which matters a lot to his countrymen in Judaism. It had to be through a promised person, Christ. That would be true of Abraham and current Judaism.
If anything was to improve the clarity of 18, I would say it was "because God had promised it to Christthat he gave it to Abraham. That is the sense. Likewise in 17a. God made a covenant (with Christ) and promised to keep it. The topic here is not the gift of righteousness for Abraham here, but the gift of the Spirit, as it was in v14 and originally in 3:2-4.
4, the absence of the Many. The Many disappear from reference at v16 but that is the official declaration of the apostle. The problem of D'ism for years has been whether they will accept this. Apparently for Judaism as well, because the plain language of 17 seemed mistaken to them. The only way it clears up is if the parties are God and Christ, and if the thing promised is the Spirit so that the mission of the Gospel proceeds and succeeds. But even after mentioning the Law, Paul repeats that the covenant was not with the Many but with the Seed, v19.
5, the parallel in Acts 13. The closest comparable passage about this is Paul in Acts 13 quoting Isaiah about the promises to David. They are given to Christ. That's how they get fulfilled. There is no expectation of their fulfillment in a sense which would be like the ancient past of Israel. They also exist for the mission of the Gospel.