Traditionally aioli is made without the eggs, it’s just an emulsion of garlic and olive oil. Nowadays there is usually an emusifier in it, but unlike with mayonnaise that emulsifier doesn’t have to be eggs. The most common one I’ve seen is with milk which you can easily switch to plant milk and make it vegan. Calling all mayonnaise-like condiments with garlic “aioli” is a very modern and I think mostly American phenomenon. I have personally never had aioli with eggs before because and I’m from Europe. So you’re actually both correct. It’s just that your husband is probably thinking of the European definition while you’re thinking of the American one.

Hi Ali, I’m so glad you enjoyed it!

Alioli is already vegetarian since it uses only garlic, olive oil and a pinch of salt.
Eggs is a modern addition only used in United States of America.

So you give it 3 stars without even trying it? Huh.