(FORTUNE Magazine) – ''Hotel Drops Veal from Restaurant Menus'' was the headline atop a UPI dispatch the other day. The story went on to recount that the Clarion Hotel in Cincinnati had taken a principled stand against veal, that the principle at issue was the harsh treatment of veal calves during their brief lives, and that ''if hotel restaurant customers ask why veal isn't on the menu, staffers will tell them.'' Unstated was whether the staffers would also be supplying membership applications for People for the Ethical Treatment of Animals (PETA), long active in the campaign against veal. Veal, and meat generally, could be in trouble. One reason for thinking so is the exponential growth of the animal-rights movement. (PETA today claims 280,000 members, up from 60 in 1980.) Combine this growth with soaring cholesterophobia among America's eaters, and vegetarianism looks like a winner. The only real question is why it hasn't come along faster. Thus far PETA and similar organizations have used most of their firepower in crusades against (a) laboratory experiments involving animals and (b) folks who wear fur coats. But PETA has always been for vegetarianism in principle, and national director Ingrid Newkirk stands ready to recite data showing that male vegetarians live seven years longer than male meat eaters. If true, that would put meat in the same mortality league as cigarettes (which appear to reduce life expectancy among 35-year-old men by around eight years). It ain't exactly so, however. The claim is based on studies of notoriously longevous Seventh Day Adventists, who do not eat meat -- but also don't smoke or drink. A big question about the animal-rights movement is whether it is capable of growing up. You would like to believe the movement has some such capability because its message is not entirely nutty and some of what it says is important. It seems a good idea for laboratory researchers and fur trappers to focus on the physical suffering, some of it plainly unnecessary, they inflict on sentient beings with highly developed nervous systems. Maybe it is even a good idea for them to think about the psychological well-being of laboratory animals, as all researchers now routinely claim to be doing when they apply for grants from the National Institutes of Health. In practice, this can mean TV for monkeys. But the movement has been arguing its case at a low level. PETA, for example, seems incapable of focusing on the costs involved in any reduction of animal suffering or of acknowledging that hamburgers, fur coats, and animal research have any social utility. Its rhetoric, oblivious to the tradeoffs, returns endlessly to the moral failings of others. Says national director Newkirk: ''If you wear fur for fashion, you are either ignorant or insensitive.'' Inevitably, the movement has attracted more than its share of crazies, and harassment of furriers and researchers has repeatedly resulted in physical violence. PETA firmly repudiates such tactics, but not all animal-rights groups are so fastidious. Stanford University's Medical School got bomb threats from the Animal Liberation Front several weeks ago, after the school's announcement that it had implanted the AIDS virus in mice. (The FBI has classified the Front as a terrorist organization.) So far, at least, the campaign against veal seems more civilized.