THe Dalai Lama, someone who thinks more deeply than I, points to his canines when people ask about eating meat.I am not for killing for pleasure but humans are omnivores

sorry but animals of all varieties have been documented as killing other animals for what appears to be sport, e.g. dolphins vs smaller porpoises, outdoor cats, dogs.
What allows animals to kill others for food? We humans are animals!

That is simply a fact, whether or not one supports humans hunting for sport.
If we are arguing the ethics of the impact on the environment two things, one there are simply too damned many humans on this planet. Population control should be #1 priority and few ever discuss it. It's always about bandaid fixes that don't really address that baseline problem, too damned many people.
2 Horticulture has its own impact on the environment (herbicides, non indigenous cash crops etc)

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That is a very real dilemma we face. Meat eaters love their meat and refuse to be vegetarians. Many people are in denial that animals have feelings and can think. In the wild the animals that are killed for food are the old and weak. New Zealand passed landmark legislation recognizing that all animals are sentient. We need to create more food sources.

Rule of nature? Evolution has decided what type of food a species needs to survive. Carnivores eat meat, herbivores eat plants, omnivores eat anything. Physically we are designed to eat (almost) anything. Digestion is another topic. I eat meat. Not an large amount, but I eat it. Some people say I won't eat meat because I love animals. Well, I love animals probably more than the average person; I also love plants. And being raised in the country with farmers all around me, I understand the history, the processes, the difference between pets and livestock. I've become more and more careful of my sources (living in a city changes the availability of food sources), but still haven't felt the 'urge' to become a vegetarian. Time will tell.

The rule of nature is that carnivores naturally prey on smaller and weaker carnivores and any and all herbivores that they can. Humans being omnivores, ie. part carnivore, part herbivore obey the dictates of carnivores for the most part. However the invention of agriculture and hence civilisation has allowed humans to also allowed humans to kill other animals for pleasure, something that is quite unusual with most carnivores. Most carnivores will kill other members of it's own species if they are perceived as competitors for territory or mates, and humans seem to not differ much here either. The concept of bullying would be only something that has come with advancing civilisation.

There is no rule, as you describe, rather in a certain environment a particular behaviour will allow a certain species to thrive, whilst in a different environment, that same behaviour could be detrimental to the species. I suspect that humans fit the latter, unless the powers that be wake up to it.

All animals (and some plants) kill other organisms for food and, when necessary, to protect one's self, family, and/or group. Killing another organism of any kind for no essential reason is destructive.