And I expect that for cows, pigs, and certainly chickens.

Certainly chickens? Do you think birds are generally less intelligent/self-aware than mammals?

Some birds, especially corvids and parrots, are among the most intelligent animal species; a number of bird species have been observed manufacturing and using tools, and many social species exhibit cultural transmission of knowledge across generations. Wikipedia

Also see the following links that indicate how similar/intelligent some other species might be:

• Bigger Not Necessarily Better, When It Comes to Brains
• Clever New Caledonian crows use one tool to acquire another
• Meet the Genius Bird: Crafty Crows Use Tools to Solve a Three-Step Problem
• Metacognitive Apes
• Chimpanzees Prefer Fair Play To Reaping An Unjust Reward
• Scientists say dolphins should be treated as non-human persons
• Evidence suggesting that humans and other primates process numbers using common cognitive skills with a shared evolutionary origin.
• Good Dog, Smart Dog
• Common fish species has 'human' ability to learn
• Octopus carries around coconut shells as suits of armour
• Altruistic chimpanzees clearly help each other out
• Amazing rats
• Ravens console each other after fights
• Missile-throwing chimp plots attacks on tourists
• How chimpanzees deal with death and dying
• Hyenas cooperate better than chimps, study finds

So far, mammals are born, they live, they experience emotions positive and negative, and they die. How much sense does it make to adopt a moral system which thinks we are wrong for just doing what nature has very many animals do for millions of years?

Morality is not a prescriptive natural law. There is no imperative here. Personally I want to minimize suffering as much as I can. That means that I am going to kill an (subjectively) inferior being to survive. But I am living in a western country, having enough money to effort a healthy diet without inflicting additional suffering for the pleasure of eating meat. Surely if you assign higher utility to eating meat than negative utility to killing other beings, that's completely rational. But you seem to be committing the naturalistic fallacy here.