We need to eat protein, but in moderate amounts. We do not have to eat a huge steak for supper. A small portion of meat or chicken or fish is adequate. And a good rule of thumb (based on Torah laws) is to always eat lighter food before heavier food. If, for example, a person wants to eat chicken and meat at one meal, eat the chicken first. Salad should be served before other food.
Unfortunately, todays meat and chicken are not usually the healthy quality that they used to be. If the beef is not grass fed or the chicken is raised on gmo feed or under unhealthy conditions, obviously that is not of the healthiest quality. Nevertheless, eaten in moderation, these foods are still good. The Torah itself, in parashat Bshalach, discusses in Rashi that we learn from the portion of the manna that nobody should eat meat to satiation. Bread however can be eaten to satiation (but again, it depends on the type of bread and method of preparing it). And, of course, the laws of kosher automatically makes the meat healthier because before meat can be accepted as being kosher, it needs to qualify in basic health matters. If an animal has an illness or certain blemishes it cannot be used as kosher meat. Kosher meat is slaughtered and then soaked and salted to remove the blood, which of course removes many impurities as well. Therefore, even meat which is not totally grass fed, can be a healthy option, particularly, if it is glatt kosher.
Fish is a healthier protein in many ways but since the oceans have become polluted and the balance of the eco system has been thrown off, much fish is contaminated with pollutants or mercury. Therefore, even fish should be consumed moderately these days and only from clean sources. For example, wild Alaskan salmon tends to be healthier than so called wild Atlantic salmon (which is usually farmed salmon or treated in some way).
Eggs are a good source of protein and the Talmud itself says nothing can beat an egg for providing all the nutrition needed. However, again this must be consumed in moderation and the best quality eggs should be sought. Grade AA is definitely important , especially if one cannot afford organic eggs. And most important is that the chickens are range free and eat food that they find outdoors (not gmo feed). So a vegetarian diet for chickens is not necessarily healthy: in fact, that often means the chickens are given corn or soy, which is not the natural or best food for chickens, and usually it is gmo feed.