Shared ground
Paul’s basic point is about order and stability: once an agreement is confirmed, later actions do not rewrite it (v.15). He uses that everyday idea to make a claim about God’s dealings with Abraham: God made promises to Abraham, and those promises were not canceled when the law of Moses arrived centuries later (vv.17–18). So, whatever “inheritance” means in this argument, Paul treats it as something God granted by promise rather than something produced by “law” (v.18).
Paul also makes a Christ-centered claim: the promises were spoken to Abraham and to his “seed,” and he identifies that “seed” as Christ (v.16). In Paul’s logic, the promise has a specific focus and reaches its fulfillment in Christ.
Where interpretation differs (only where needed)
One difference concerns what kind of “agreement” Paul is comparing God’s promise to. Some read Paul as thinking of a contract-like covenant: once ratified, you cannot add conditions later. Others think he is closer to a will or inheritance arrangement: once established, it stands, and it controls how the inheritance is received.
Another difference concerns how Paul’s “seed” argument works. Some think Paul is building a strict argument from grammar (singular vs. plural). Others think he is using Scripture’s wording in a more rhetorical way to highlight what the whole Abraham story was always pointing toward—its culmination in one representative person, Christ.
Why the disagreement exists
The Greek word Paul uses for “covenant/agreement” can overlap with both “covenant” and “will,” and the passage itself mentions “inheritance,” which can push readers in either direction (vv.15, 18). Also, in Genesis the term “seed” often functions as a collective (descendants as a group), so Paul’s focus on the singular raises a real question: is he making a technical point about wording, or a theological point about fulfillment? (v.16).
What this passage clearly contributes
Explicitly, the text says the law came later (v.17) and therefore cannot annul the earlier promise (v.17). It also draws an either-or conclusion about basis: if inheritance is “from law,” it is not “from promise,” and Paul insists God granted it to Abraham by promise (v.18).
Theologically (as an inference grounded in Paul’s statements), the passage frames the Mosaic law as unable to overturn God’s prior commitment, and it ties the promise’s fulfillment to Christ as the identified “seed” (v.16). This supports Paul’s larger argument in Galatians 3 that belonging to Abraham’s story and receiving what God pledged is anchored in God’s promise, not in adopting the later law as the controlling basis (vv.17–18; compare Galatians 3:6).