A little googling makes it seem that this likely comes from some interpretations of the Bible that put a prophetic slant on the story of Jacob and Esau. With Esau as the "father" of the Arab people, and the split between the two brothers being emblematic of the hostility between Arabs and Israel over Palestine. All of which glosses over the difference between Arab and Muslim, among other problems with it.
The same googling leads me to think that anyone who takes this interpretation seriously is likely to be what I would personally label as 'Christian nutter'. That seems to match with my impression of Ben Carson, so it makes sense that he would really believe what he's saying. He's not making a mistake, he's just firmly planted in the world of Christian mythology, instead of history.