Some of the Fathers have written that as a result of the fall, it is extremely difficult for us to exist without the help of our fellow creatures, who give of their lives and substance to sustain us. It is simply difficult to maintain high levels of physical activity that the fallen world requires of us ("sweat of the brow" as per Genesis, etc...) without animal products.
It is clear that the Church has never recommended, let alone required, a complete abstinence from meat outside of the context of spiritual struggle -- i.e. monasticism. I think that it isn't uncommon, however, for Orthodox Christians, knowing from living as vegans 1/3 of the year that one can function without meat for extended periods of time, to carry this out further and do without meat much of the rest of the time as well.
It is in part because of this that the forbidding of fasting during certain seasons arose to mandate moderation in all things.
That much is clear. But there is nothing in the meat per se that is life-saving. The problem with strict vegetarian diets is that they cannot provide essential amino acids some of which are produced only in animals and not in plants, and are absolutely, as the name implies, essential for the normal functioning of our bodies.
We can get them, however, from milk and cheese, but a strict vegetarian diet is difficult, and the weight of meat accounts to some extent to the fullness we associate with 'satiation.' Meats also provide readily available iron needed for red blood cell formation (although one can get that from green leafy vegetables and strawberries). Then there is definitely a taste for "flesh" that is almost universal -- and may have something to do with our fallen nature.