To give a human example, brothers: even with a man-made covenant, no one annuls it or adds to it once it has been ratified. Now the promises were made to Abraham and to his offspring. It does not say, “And to offsprings,” referring to many, but referring to one, “And to your offspring,” who is Christ. This is what I mean: the law, which came 430 years afterward, does not annul a covenant previously ratified by God, so as to make the promise void. For if the inheritance comes by the law, it no longer comes by promise; but God gave it to Abraham by a promise.
Paul is offering a defense of what he has taught, that the Galatians have drifted away from. Paul preached a gospel message of freedom from the law, where our relationship with God is no longer based on a set of rules and regulations, but is now a relationship based on a love for God that guides our thoughts and actions. This relationship supercedes the law.
So Paul creates an analogy, based on something that they should understand, human law. Even with man, once a covenant is established, no one can change it on a mere whim. Whether it be the decree of a king or the constitution of a country, no one can modify that on their own.
Promises were made to Abraham and his offspring (singular). Paul says that that offspring refers to one, and that one is Christ. It was not for another 430 years after the promise that the law came into existence, so how can the law be a means of fulfilling the promise? The law does not change or fulfill the promise, therefore our fulfilling the law (if that were even possible) does not void the promise, nor does it enable us to fulfill the promise.
He does on show that if our inheritance (salvation) is through the law, then inf fact, God has broken His promise that He gave to Abraham. And God does not break His promises.
So why, Galatians, Christians, Brothers, are you seeking to follow and external obedience that in itself has nothing to do with your salvation?
God does not break His promises.