Heck, (and I’m not sure if I agree with this), I once heard someone say they were a vegetarian that occasionally eats meat.

There's also a separate term for it: Flexitarian.

I imagine, it's such a popular stance, because it deals well with the social expectation to eat meat, which is typically the biggest barrier for people to go vegetarian. For example, you can not eat meat while you're cooking for yourself, but then have it when you're going out with friends or family.