Animal rights activists don't eat meat and are vegan, but the public often doesn't understand their objections to meat. With so many campaigns focused on cruel factory farming practices, the media and the public tend to focus on the animal welfare issues more than animal rights issues.
Animal Rights v. Animal Welfare
Animal rights is the belief that animals have a right to live free of human use and exploitation. The belief is based on the realization that animals are sentient (capable of suffering) and that speciesism (exploiting nonhuman animals just because they are not human)is wrong. This philosophy applies to all animal uses, including food, circuses, zoos, animal testing, hunting, and clothing. Recognizing the rights of animals is not about exploiting them in a more humane way; it's about not exploiting them in the first place.
The public dialogue about how we treat animals is dominated by an animal welfare perspective that focuses on better treatment of the animals. The animal welfare position is that humans have the right to use animals for our own purposes as long as the use is not too frivolous and the animals are treated humanely. Within the animal welfare position, there is a spectrum of positions, and while one person may think that fur is too cruel, another may think it's OK to wear fur as long as the animals were treated and killed "humanely."
Some animal rights advocates support animal welfare campaigns such as eliminating gestation crates, veal crates and battery cages, but recognize that such reforms only reduce suffering. These reforms do not make meat acceptable to animal rights activists. Some animal rights activists support these reforms also because they believe that the reforms raise awareness about animal isssues and will lead to a more vegan world in the future. Other animal rights activists do not support these reforms because they believe that animal welfare reforms serve to further reinforce animal use, and their efforts and resources are better spent promoting veganism.
Meat, Humane Meat, Laboratory Meat and Animal Rights
While animal welfare campaigns have focused on better treatment of the animals, such as larger cages, no cages, or more humane slaughter, the animal rights position is that we do not have the right to imprison and slaughter animals for our own use, no matter how big the cages.
While those concerned about cruel factory farming practices might choose "humane meat" or organic meat, any use or slaughter of animals infringes on the animal's right to be free of human use and exploitation. Even if the animals roamed free on wide pastures, breeding, keeping and killing them violates their rigts. A grass-fed cow with acres to roam is certainly better off than a cow in a crowded feedlot, but the grass-fed cow still suffers when slaughtered. They also suffer when they are branded and confined.
For the same reasons, animal rights activists will not eat laboratory-grown meat when it hits the market. As the technology now exists, animals must be killed in order to get the cells that are used to grow muscle tissue in a laboratory. Animal products are also used to feed the tissue culture. Lab meat cannot be considered vegetarian or vegan because it still requires animal products and animal deaths to be produced.
These are the same reasons why animal rights activists oppose other animals uses, such as milk and eggs. Even if the animal is not killed for the product, they suffer in captivity and are eventually slaughtered when they get older and their milk and egg production drops.
In addition to animal rights, there are also health and environmental reasons to avoid meat. From an animal welfare perspective, there are also concerns specific to cows, pigs, chickens, wild-caught fish and farm-raised fish.