Why did the pre-Islamic Arabs identify themselves as descendents of Ishmael?

Who are the modern day descendants of Esau?

There is a Jewish tradition stemming from the Talmud, that the descendants of Esau would eventually become the Romans, and to a larger extent, all Europeans.

What nation is Ishmael the father of?

Ishmael, commonly regarded by both Jews and Arabs as the progenitor of the Arabs, is considered a messenger and a prophet (rasūl nabī) in the Qurʾān (e.g., 19:54).

Where in the Quran is Ishmael mentioned?

Surah 37:105 reads: “Thou hast indeed fulfilled the vision”, suggesting that the sacrifice has occurred. Verse 107 reads: “And we ransomed him with a great sacrifice.” The implied “him” is Ishmael. Thus, like Isaac in the biblical account, Ishmael was sacrificed, yet lives.