President Hosni Mubarak did not even wait for President Obama’s words to be translated before he shot back. “You don’t understand this part of the world,” the Egyptian leader broke in. “You’re young.” Mr. Obama, during a tense telephone call the evening of Feb. 1, 2011, had just told Mr. Mubarak that his speech, broadcast to hundreds of thousands of protesters in Tahrir Square in Cairo, had not gone far enough. Mr. Mubarak had to step down, the president said. Minutes later, a grim Mr. Obama appeared before hastily summoned cameras in the Grand Foyer of the White House. The...