Emulsifying extra virgin olive oil with a food processor causes the [insert sciency term for green plant stuff here] to disperse and will overwhelm the mayonnaise with bitterness. You want to use a neutral-flavored oil like pure/light olive, avocado, macadamia, or grapeseed. Pure olive oil is the cheapest low-PUFA option (a heavily saturated fat like coconut oil will break)..
Extra virgin olive oil is fine if you're making an aioli or pesto with a mortar and pestle, though. It's also ok for quick & low heat cooking like sauteed greens, just don't let it get smoky.
“The whole concept of a macronutrient, like that of a calorie, is determining our language game in such a way that the conversation is not making sense." - Dr. Kurt Harris