One reason it is so high is math. Your progenitors double every generation going back. By the time you get back 30 generations (roughly 1000 years ago), you have 67 million potential ancestors, or roughly two-thirds of the entire estimated population of Europe at the time.
Of course lack of mobility which led to cousin marriages and the like reduced that actual number considerably and that is why it is 1 in 12 rather than 2 in 3.
Exactly! Thanks for that great explanation!