What is the virtue of the Prophet's lineage, and why was Umar ibn al-Khattab keen on tracing his lineage, despite sharing Ka'b ibn Lu'ayy with him?

The lineage of the Prophet, peace and blessings of Allah be upon him, has many characteristics. He was the elite of Banu Hashim, the lineage and core of Quraysh, and among the noblest of Arabs, the most honored in terms of kin from both his father and mother, and from the people of Mecca. Judge Iyad mentioned the nobility of his lineage and the honor of his land in "Ash-Shifa bi Ta'rif Huquq Al-Mustafa" (Healing by the Recognition of the Rights of the Chosen One).

There are prophetic hadiths that confirm the nobility of his lineage, peace and blessings of Allah be upon him, among them: - The hadith of Abu Hurairah, may Allah be pleased with him: «I was sent from the best generations of the Children of Adam, generation after generation, until I was in the generation from which I was born.» (Narrated by Al-Bukhari). - The hadith of Al-Abbas, may Allah be pleased with him: «Indeed, Allah created creation and placed me among their best, and among the best of their generations. Then He chose the tribes and placed me among the best of tribes. Then He chose the houses and placed me among the best of their houses. So I am the best of them in soul, and the best of them in house.» (Narrated by At-Tirmidhi, who graded it good; Al-Albani graded it weak). - The hadith of Wa'ilah ibn Al-Asqa', may Allah be pleased with him: «Indeed, Allah chose Ishmael from the descendants of Abraham, and He chose Banu Kinanah from the descendants of Ishmael, and He chose Quraysh from Banu Kinanah, and He chose Banu Hashim from Quraysh, and He chose me from Banu Hashim.» (Narrated by Muslim).

As for Umar ibn Al-Khattab's keenness, may Allah be pleased with him, on the Prophet's lineage, peace and blessings of Allah be upon him, it was due to the Prophet's saying, peace and blessings of Allah be upon him: «Every lineage and kinship will be cut off on the Day of Resurrection except my lineage and kinship.» (Narrated by Al-Hakim and others, and graded authentic by Al-Albani). Umar married Umm Kulthum, daughter of Ali ibn Abi Talib, may Allah be pleased with them both, one of the daughters of Fatimah Az-Zahra, may Allah be pleased with her, to attain this honor, as mentioned by Al-Munawi in "Fayd al-Qadir" and "Samt al-La'ali".