The tradition to wear a kippah is not derived from any biblical passage. Rather, it is a custom which evolved as a sign of our recognition that there is Someone “above” us who watches our every act.
Talmudic Precedent
The Talmud1 relates that a woman was once told by astrologers that her son is destined to be a thief. To prevent this from happening, she insisted that he always have his head covered, to remind him of G‑d’s presence and instill within him the fear of heaven. Once, while sitting under a palm tree, his headcovering fell off. He was suddenly overcome by an urge to eat a fruit from the tree, which did not belong to him. It was then that he realized the strong effect which the wearing of a kippah had on him.
In Talmudic times, the practice of wearing a headcovering was reserved for men of great stature. In later generations, though, it became the accepted custom for all Jewish men to wear a kippah at all times, and especially during prayer. As with all Jewish customs, once they become a universally accepted Jewish practice, they become halachically obligatory.
According to some opinions, since wearing a kippah has become a form of distinction between Jews and non-Jews, failure to wear a headcovering falls under the prohibition of “you shall not follow their statutes.”2
Click here for more about the kippah.
I was taught by a cousin who did his Jewish History PHD at Harvard under Prof. Yerushalmi,
that the Jews in Ashkenaz copied the Kippa from Catholic Clergy, and that Rabbanei Sefarad in the 13th & 14th C. forbade the use of Kippot as 'Minhag AKUM' {Behavior of non-Jews (literally, Ovdei Cochavim veMazalot - or Worshippers of Stars and 'Horoscopes').
Jews covered their heads with their Tallit [Prayer Shawl] during prayer, etc.
this seems historically legit... hmm, I'm surprised and Puzzled by the Rabbi saying if it custom becomes broadly accepted it becomes Halachah... Curious, how can one add to the Torah? or take away from the Torah?