Look, I am decidedly NOT a vegetarian. I love meat and, like most people, will likely continue eating meat until an equally delicious alternative is available at a reasonable price. I also get that people have problems with the perceived self-righteousness of some vegetarians and vegans.
However, it absolutely made sense that a guy like Superman, who has the ability to see life on a level that we can barely comprehend. Of course a guy like that wouldn't be down with eating meat, particularly when it's very likely that he doesn't need to eat at all.
But, when Birthright was supplanted by Secret Origin, I am pretty sure that Clark has been depicted eating meat again. Why didn't it stick around?