As to the black belt being selected as the high rank belt, some think Kano borrowed the concept from Japanese high school sports where advanced competitors were separated from beginners in swimming tournaments by a black ribbon worn around their waist.
As to the selection of the red/white sectioned belt, the Japanese usually divide groups into red and white sides. This preference comes from the Genpei War, which was a dispute between two rival clans, the Genji and Heike. The Genji used white flags to identify their troops on the battlefield, while the Heike used red flags. In our modern day competitions, we still differentiate the competitors using white and red ribbons.
Kano also studied the I Ching, Book of Changes. The I Ching is basically a collection of moral and political wisdom based on the concept of mutual opposites, referred to as Yin and Yang. Kano's selection of red-and-white colored belts may have been a symbolic representation of the principle of harmony suggested by the balance of Yin and Yang.