Some people try to make a religion out of it, but I choose to eat vegan because it's healthy. I could not care less that an animal is confined in a cage. Think about the people that are confined in pretrial custody... innocent until proven guilty, yet treated guilty until proven innocent.
Yes, in my world, people come first. If there's a burning apartment building and there is a baby in the room on the left and a box of kittens in the room on the right, and I only have time to bust down one door, and the door to the kittens is unlocked, I'm gonna save the human baby first.
If a person is going to use their voice to draw attention to the plight of cows when there are still people suffering, then I think that person has some messed-up priorities. If no one ate beef, then it's likely no cows would exist in the U.S. At least the cow got to exist. All creatures grow spiritually from the pain they experience. Without pain there would be no joy.
Honestly, no one really likes meat. That's why they cook it and salt it... to change the flavor. A person was incarcerated and was fed bland food (no salt) because the Governor of that state wanted to make sure the incarcerated were being punished and did not enjoy any part of their stay. (It didn't seem to make a difference that most of the people in the jail were still awaiting trial and were not being punished; they got to experience the same treatment as the punished). But by adding salt to the food it tasted so much better that the person realized they had never really craved meat; it was the salt they had always craved. This was relayed to me, and I too realized that I only ever liked cheese, sausage, bacon, etc. because of the spices and the salt. I did some research and discovered that when protein and salt are heated together, they form monosodium glutamate, or MSG. MSG is a drug that is like a halucinogen for your tongue. It makes anything taste good.
Some people aren't as affected by certain drugs as others due to their genetics. So you possibly don't like meat because you don't like MSG. That's good. Neither meat nor MSG are any good for you anyway.
In any case, to directly answer your question, you are a vegetarian if you don't eat meat. You are a vegan if you don't eat any animal products, including milk, mild products, eggs, etc.
I saw a youtube video where someone claiming to be vegan used natural honey, but honey is made from bees, so I don't know if that's an exception or what.
Lots of people call themselves Christian but then they continue in sin, so basically you can call yourself whatever you want; it doesn't even have to be true.