You can make mayonnaise with any kind of oil, but if you choose unrefined extra-virgin olive oil, don’t be surprised if the emulsion breaks after a few hours—for reasons too chemically complex to explain here, unrefined, old, or improperly stored oils produce unstable mayo. If you really want olive oil-flavored mayonnaise, try cutting unrefined extra virgin oil with neutral-flavor refined oil, or use a refined olive oil.