Why does Paul say the inheritance is not based on the Law?
The inheritance is not based on the Law because it rests on God's promise to Abram. If it were by the Law, it would no longer be by promise. The Law could not fulfill the promises; it could only condemn Israel. God gave the covenant based on promise, not Law.
Les explains from Galatians 3:17–18 that the inheritance cannot be based on the Law, because if it were of the Law, it would no longer be based on promise. He points back to God's dealings with Abram, where God gave promise after promise—'I will, I will, I will.' The Law could not fulfill any of those promises; all it could do was condemn Israel. So if the Law was going to do the job, it would no longer be a promise. But God gave the covenant based on promise, promise. Les also notes the Law was added 430 years after Abram left Haran and went into Canaan, until Moses led Israel out and they received the Law at Mount Sinai. It was added 2,500 years after Adam, for a valid reason.
For if the inheritance be of the law, it is no more of promise: but God gave it to Abraham by promise.
More Questions
What happens to the promise if the inheritance comes by the Law?
If the inheritance is by the Law, then it is no longer based on promise.