Scott Adams answers:
My hypothesis is that apologies are a way for humans to determine their status in society. A king and queen never apologize for their actions because they don't need to. But the server at your local restaurant apologizes even when he knows the customer is in the wrong, because the server has a lower status than his boss, who in turn has a lower status than the customers.
When you're trying to determine the status of people, apologies are reliable markers. In the Limbaugh/Fluke situation, society is asking Limbaugh to acknowledge that despite his many listeners, and despite his alleged influence on politics, his status is lower than that of the 3.5 billion women on the planet. Limbaugh's apology clarified his status, like a submissive dog lowering his head when a more dominant dog comes near.