Actually Saladin belonged to the Rawadid dynasty/tribe which is Arab in origin. Later some of its branches, including the one Saladin belonged to became Kurdified and others Arabized (returning to their origin).
"Saladin was born in
Tikrit in modern-day
Iraq. His personal name was "Yusuf"; "
Salah ad-Din" is a
laqab, an honorific epithet, meaning "Righteousness of the Faith."
[12] His family was of
Kurdish ancestry,
[4] and had originated from the city of
Dvin in medieval
Armenia.
[13][14] The
Rawadid tribe he hailed from had been partially assimilated into the Arabic-speaking world by this time.
[15]"
https://en.wikipedia.org/wiki/Saladin
Tikrit and Arbil are ancient Semitic lands too. Many Kurds are originally of Arab/Assyrian origin who became Kurdified. Kurds are not a homogenous people.
"According to
Minorsky and
Bosworth, the Rawadids were originally of Arabic ancestry, and arrived in the region in the mid eighth century,
[6][7] but they had become Kurdicized by the early 10th century and began to use
Kurdish forms like
Mamlan for Muhammad and
Ahmadil for Ahmad as their names
[8][9]"
https://en.wikipedia.org/wiki/Rawadid_dynasty
Minorsky was the foremost expert on Kurdish history of his time and Bosworth was (he died in 2015) one of the leading experts on Kurdish history.
So most likely he had both Kurdish and Arab ancestry as Arab-Kurdish intermarriages in that region of the Middle East, even back then, were fairly common.
"Sultan Saladin spoke both Arabic and
Kurdish, and likely
Turkish as well.
[93][94] According to Yasser Tabbaa, an anthropologist specializing in medieval Islamic culture,
[95] the Ayyubid rulers who reigned in the late 12th-century were far removed from their Kurdish origins, and unlike their Seljuq predecessors and their Mamluk successors, they were firmly "Arabized."
Arabic culture and language
[96] Arabic culture and language
[96] formed the main component of their identity instead of their Kurdish heritage.
[97] Arabic surnames were much more prevalent among the Ayyubids, a tribe that had already been partially assimilated into the Arabic-speaking world before its members came to power, than non-Arabic names. Some exceptions included the non-Arabic surname
Turan-Shah. Most of the Ayyubid rulers spoke fluent Arabic and a number of them, such as az-Zahir Ghazi,
al-Mu'azzam Isa and the minor emirs of Hama, composed
Arabic poetry.
[98]"
https://en.wikipedia.org/wiki/Ayyubid_dynasty
Another thing, his descendants continue to live in the Arab world and are now Arabs and consider themselves Arabs. Descendants of the Ayyubid dynasty live in Jordan, Sham and KSA today. None in majority Kurdish lands. They are know as Al-Ayyubi/Ayoubi and one of my childhood friends belonged to this family...