His Mama was white. His Daddy was mostly Arab. Any black in his family is mainly due to African females added to the harem. BO's Kenyan tribe had close family ties as well as commercial tribes to Arab slave traders. Google the history of Zanzibar and German East Africa for more details.
The slave trade put BO's tribe near the top of the pecking order. This is the reason for the extreme animosity to Great Britain in general and Winston Churchill in particular.
The slave trade was extremely lucrative for BO's tribe. That is why they were clustered near Zanzibar and the coast where most of it took place.
The Brits ended the slave trade in two phases. First, when they were forced to colonize Kenya in 1888 to stamp out this indignity. Second, when they gained full control of German East Africa and Zanzibar after World War I.
Most of the African side of BO's lineage comes from his patriarchal line's wives. One of the fringe benefits of trading slaves was being able to cherry-pick women from a new crop of captives to add to your harem.
This ended when the Brits took full control over the former German areas after World War I. As a result, most of the slave trading members of BO's tribe had to move to less pricier real estate in the interior of the country and take up the more menial work of herding goats and cattle.
Now you know why BO's fathers hated the British with a purple passion and Winston Churchill in particular. You also understand why his claim to African ancestry is based mostly on forced marriages of slaves added to his father's harems.
Good, succinct racial background on Obama!