One reason why the winner of the popular vote might not win the presidency is that

Due to the flaws on Electoral College, there will always be a possibility that the winner of the popular vote may not win the presidency. This has already occurred four times and the most recent in 2000. This is because of the winner take all factor which means that any votes won by the loser of the popular vote are not replicated in the electoral vote. Like in 2008, Barack Obama won only in the 51 percent of the popular vote in Ohio but still, he won all of Ohio's electoral votes even though most of the Ohioans voted for John McCain.