Humans naturally are omnivores, which is shown in out tooth structure and the length of out intestines. So vegetarianism is actually deviation from our true nature. I eat what tastes good. Since i have been bought up on a vegetarian diet i am more comfortable with it and dont like the taste of non veg at all.
Now i will go on point wise:
1)Whether Non veg is healthier or not is a moot point because "healthy" depends on your diet. Both veg non veg and veg can be healthy or unhealthy. But non veg does have some nutrients that are lacking in a vegetarian diet.
2)Eggs, well i think they are a middle ground like viruses(they are neither living nor non living in truest sense)
Eating any food group is a personal choice. Plants are living too, it is true, so if you eat a chicken or a plant or anything else for that matter you are no different because we all are following the food chain, we need to survive and for that we need to eat. Biologically it makes no sense in eating the creatures that are on the same level as you on the food chain because of, Let me explain in detail. Say there is a plant it takes energy from the sun as it requires very little for its survival maximum is stored. A goat eats this plant it gets the excess energy the plant had. Now the goat uses a part of this energy for its survival and stores the excess. A tiger then eats the goat so it gets the excess of the goat, it then uses it a part of it up and stores the rest. So as you can see the energy becomes so less as it reaches the secondary consumer it doesnt make sense to eat them because the energy we get from them would be so less. Also there is this effect called bio-magnification.
Vegetarianism is flawed in itself because of the ideology it promotes. They tell you you are superior since you are a vegetarian because you dont kill others for food, but actually that is how our world is built, you have to kill something(be it plants, bacteria, animals) to eat and survive there is nothing wrong with that. So if you choose veg choose it because you like it nothing else, you are in no way different that a person eating anything else.