Fake/Vegetarian eggs are priced the same here, so I made the switch and am only using fake eggs now for most of my cooking.
arent eggs already vegetarian
The usage of the term "vegetarian" in the US is not consistent enough to come up with a precise definition, probably due to the mixture of so many cultures bringing their variation and translations. So it's always good to clarify on particular food items in my experience. Some will consider eggs part of a vegetarian diet, others will be practically offended at the ridiculousness of the idea.
Huh? I'm American and even used to work as a professional line cook. Vegetarian has only ever meant "no meat products" to me. Vegan means "no animal products of any kind", and anything else requires a more specific phrase like "I'm vegetarian, and also I don't eat eggs", or "I can't eat any dairy products at all", or whatever.