Considered by many to be the gold standard for human dietary practice, the key reason for this diet is usually ethical, religious or environmental; not primarily health based. It's very difficult but not impossible to be both vegetarian and healthy. That's why in practise most vegetarians are not very healthy, despite what they might personally claim.
Many vegetarians have thought very carefully about what they are doing, and are knowledgeable about their dietary practice. I don't pretend to know anything like as much as they do. What I can do is report the science I've read about.
Vegetarian diets range from the diet I ate for many years, based on "Eat a variety of food, mostly vegetables" which for our family meant; red meat almost never, chicken once a week and fish once a week. We imagined that a vegetarian diet was desirable but we were not strongly committed to it. At the other end of the scale are vegan diets that eliminate all meat, dairy foods and even eggs.
Most vegetarians I'm told do eat fish, but perhaps only once a week.
The chief advocates of a vegetarian diet through history often come to the diet because of religious belief. Many religions have sects that encourage a vegetarian lifestyle, like the Seventh Day Adventists, for instance. In science, notable advocates have been Nathan Pritican, Dean Ornish and Caldwell Esselstyn; and more recently Colin Campbell.
In my reading I seem to have come across quite a number of very knowledgeable able people who at some time were committed vegetarians. At least two with a 20 year history as vegetarians. Both the people I'm talking about eventually became sick and couldn't resolve the problem until they changed their diet. Of course they now speak of vegetarian diets with caution. That's all I can do too. There are strong negatives that make being a vegetarian a rod for your own back.
A recent UN report claims that as the world's population approaches over 9 billion people by 2050, it will not be possible to sustain the per capita consumption of meat and dairy products that we are currently eating. We will deplete our resources if we attempt to do so, noting that "agriculture, particularly meat and dairy products, accounts for 70% of global freshwater consumption, 38% of the total land use and 19% of the world's greenhouse gas emissions."
The facts in the previous paragraph are open to challenge. That doesn't take away the problem. The world is over-populated if all people are to eat a healthy diet based on animal protein and animal fats. If the LCHF diet is the best human diet, we are already in serious trouble. If the mixed American Standard Diet is your healthy food option, we're in deep trouble. If people world wide are to eat a vegetarian diet, there's no chance that they will eat the sort of diet very knowledgeable people can choose for themselves. The availability of meat gives people with less expertise a chance to get the nutrition they need. Vegetarian diets might be able to provide sustenance for people, but they are unlikely to be healthy as a result. (To keep things in perspective they are not healthy now, even in advanced societies.)
If this is the paradigm you prefer; nothing anyone can say will convince you otherwise. Open Future Health notes the evidence from human physiology against vegetarian diets here. If that isn't convincing, we do understand the high principles you are trying to live by.