No - The consumption of livestock products should be diminished but not eliminated
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It is impossible for everyone to stop eating meat
In some parts of the world, meat and fish consumption are a means of survival.
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Meat consumption could never end worldwide because many groups of people rely on meat consumption to survive. For instance, many peoples who are indigenous to polar environments had scarce access to fresh fruits and vegetables. Therefore, they must rely on meat and fish for sustenance. An example of this is the Eskimo tribes of Alaska and northern Canada, who need the meat of seals, walruses, fish, and whales to survive.  Another example of this is the Maasai, a pastoralist tribe in Kenya and Northern Tanzania. The people of this tribe survive almost entirely off of milk, meat and blood.  In a less drastic sense, many people need meat to survive simply because they cannot afford to buy other forms of protein. Soy or nut based alternatives to meat are often far more expensive than real meat, and many people don’t want to give up meat if there’s no cheap alternative. Additionally, there are many key nutrients in meat that we need to survive that cannot be found in plants. These nutrients include vitamin B12, creatine, carnosine, vitamin D3, docosahexaenoic acid, heme iron, and taurine. The only way that someone who does not eat meat can get these nutrients is through the use of vitamins or artificially enriched foods.  These can be too expensive for some people to afford, making it easier to just get those nutrients from meat. For these reasons, there are some groups of people who rely on meat consumption to survive. If we as a species decided to stop eating meat, the survival of these groups would be threatened. Thus, we should not try to eliminate all meat consumption.
In arguments about meat consumption for environmental reasons, people in favor of stopping meat consumption are hardly ever concerned with stopping all meat consumption worldwide. Environmental activists generally target factory farms and large scale meat production corporations, not small groups of Indigenous people. The fact that it's impossible for everyone to stop eating meat is a straw man argument, because the vast majority of people who are concerned about meat consumption for environmental reasons are not concerned with small groups of people who hunt for meat in the wild themselves. In a similar way, many environmental activists are completely fine with small family farms eating meat; it's factory farms that are the main target. Factory farms and other large scale meat production corporations are what needs to be stopped to save the environment, not every single individual instance of meat eating.