In Paul's letter to the Galatians, he talks about (among other things) how God's promise to Abraham was fulfilled in Christ. Galatians 3:16 reads (in the NRSV; other translations may say "seed", "progeny", "descendants", etc.):
Now the promises were made to Abraham and to his offspring; it does not say, "And to offsprings", as of many; but it says, "And to your offspring", that is, to one person, who is Christ.
Elsewhere he says that "those who believe are the descendants of Abraham" (3:7) and "if you belong to Christ, then you are Abraham’s offspring, heirs according to the promise" (3:29).
In Genesis, there are several promises (or repetitions of a promise) made to Abraham, including:
Then the Lord appeared to Abram, and said, "To your offspring I will give this land." (12:7)
On that day the Lord made a covenant with Abram, saying, "To your descendants I give this land" (15:18)
"I will establish my covenant between me and you, and your offspring after you throughout their generations, for an everlasting covenant, to be God to you and to your offspring after you. And I will give to you, and to your offspring after you, the land where you are now an alien, all the land of Canaan, for a perpetual holding; and I will be their God." God said to Abraham, "As for you, you shall keep my covenant, you and your offspring after you throughout their generations." (17:7-9)
"I will indeed bless you, and I will make your offspring as numerous as the stars of heaven and as the sand that is on the seashore." (22:17)
It seems that in Genesis, the promises are actually speaking about many descendants and not just one person, regardless of the grammatical detail. Certainly the appearances in chapters 17 and 22 are talking about many people in many generations.
So isn't Paul just making a totally unsupported argument? And why does he make it at all, given that a few verses before and after, he is happy to consider plural offspring (all believers)?