Why "extra virgin" olive oil?

Because it's the best!

Extra virgin olive oil is obtained solely by mechanical or other physical means in conditions which do not alter the oil in any way. The olives and the oil pressed from them have not undergone any treatment other than washing, decanting, centrifuging and filtering. This is the only way to preserve the natural aroma and fullness of taste, and because only the best ripe and sound fruit can be used, extra virgin oil comprises only about 10 percent of annual production. With year-to-year variation, about 50 percent of the oil produced is of such poor quality that it must be refined by use of charcoal or other chemical or physical filters to produce an edible product.

By the way, the still-used term "cold-pressed" is actually an anachronistic and unregulated description. Long ago when oil was made in vertical presses, the paste was pressed to make olive oil (called the "first press") and then mixed with hot water or steam and pressed again to remove more oil. This "second pressing" was never as flavorful because heat evaporates the most delicate components of taste and aroma. Today, the olives are allowed to warm to room temperature (olives are harvested in the winter when it is cold) before being centrifuged. Neither heat nor any chemical is allowed in pressing extra virgin olive oil. Because consumer education is a slow process, the term "cold pressed" still appears as a quick assurance.