When is the best time to harvest olives for quality extra virgin oil?

Quality is the ultimate goal. To be successful in this endeavor, olives are harvested at the greenish yellow stage of their maturity (therefore, not really ripe at all) as early as possible in the harvest season. At this stage of maturity, their oils have a high content of healthy polyphenols, which makes them more bitter and pungent than if they were from ripe olive. They also have a fresher, crisper, and cleaner flavour that is quite herbal. 
However, the greener the olive, the less oil it contains, which makes the oil more difficult to extract. During maturity, when olives turn completely red or slightly purple, they have lower polyphenol content and their oils come out less bitter and less pungent. These olives have a taste more reminiscent of hazelnut, butter and tropical flavors. When there are no blemishes, the perfect time to reap the rewards really comes down to personal preference and style.

A pressed black olive oil will not have the qualities required to be categorized as a high quality extra virgin olive oil. The oils of poorer quality will then be classified either as virgin olive oil, lampante or as refined oils having undergone chemical and physical treatments.

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In conclusion

The time at which olives are harvested depends on the use for which they are intended. An olive intended for the production of extra virgin olive oil will be harvested at the start of the harvest season, while an olive intended for the production of lampante oil (non-edible oil) will be harvested at the end of the season. Between two to three months may elapse between these two harvests

Reference:

Paul Vossen - International specialist in olive oil