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It might be because they believe they have an ethical responsibility to limit the suffering of animals raised for slaughter, for example.That sounds more like a religious argument. At the extreme, some people don't believe that it matters ethically how animals are treated, and there are certainly many people who adopt an "out of sight, out of mind" attitude, or try to only eat meat from animals raised and slaughtered as humanely as possible. People are of course free to make a value judgment on these attitudes, but preaching vegetarianism/veganism on those grounds sounds too much like religious proselytizing for my taste.
I think it's fine and useful to promote non-meat diets by arguing that meat production (as we currently do it) is devastating to the environment, but religious/emotional preaching is IMO what gives a lot of vegetarians/vegans a bad name.