It's a common enough scenario. A vegetarian has been invited to a friend's place for dinner. The host forgets that the guest is a vegetarian, and places a pork chop in front of her. What is she to do? Probably her initial feelings will be disgust and repulsion. Vegetarians often develop these sorts of attitudes towards meat-based food, making it easier for them to be absolutists about shunning meat.
Suppose, though, that the vegetarian overcomes her feelings of distaste, and decides to eat the chop, perhaps out of politeness to her host. Has she done something morally reprehensible? Chances are that what she has been served won't be the kind of humanely raised meat that some (but not all) ethical vegetarians find permissible to consume. More likely, it would be the product of cruel, intensive factory farming. Eating the meat under these circumstances couldn't then be an act of what the philosopher Jeff McMahan calls "benign carnivorism." Would the vegetarian guest have done something wrong by breaking her own moral code?
Most vegetarians are concerned about animal suffering caused by meat consumption, or about the impact of factory farming on the environment. For simplicity's sake, I will consider only the case of animal suffering, but the same argument could be applied to the other bad consequences of today's practices of factory farming, including, for example, greenhouse gas emissions, inefficient use of land, and use of pesticides, fertilizer, fuel, feed, and water, as well as the use of antibiotics causing antibiotic resistance in livestock's bacteria which is then passed on to humans.
Because eating meat typically supports the practice of raising animals in factory farms where they are inhumanely treated and killed, eating meat is likely to contribute to animal suffering (or to the other bad consequences of factory farming). Now, if we agree that one of the good reasons for being vegetarian is that eating meat to some degree encourages practices that cause animal suffering, then at a first glance it might seem that eating meat only rarely is morally permissible (but see the philosopher Shelly Kagan for a counterargument) because it is very likely that eating meat only occasionally will not have any impact on the amount of suffering inflicted on animals.
However, by not eating meat, and especially by not eating meat when they are offered it in front of non-vegetarians, vegetarians send out a message to other people. By sticking to their ethical commitment, vegetarians signal that there is something wrong with being a carnivore, thus prompting other people to consider the morality of their habit of eating meat and perhaps even persuading them that consuming meat is wrong. In other words, the positive impact of being a vegetarian, in terms of reduction of animal suffering, might be amplified when vegetarianism is publicly defended and demonstrated in social contexts. And, conversely, making exceptions to vegetarianism might convey the message that eating meat is not so bad after all. If even vegetarians sometimes eat meat, then eating meat can't be so reprehensible from a moral perspective, can it? So perhaps the guest who ate the pork chop was morally wrong for this reason: She sent out the wrong message to the people who were having dinner with her.
But it isn't as simple as that. Avoiding meat in all circumstances, including in the circumstances in which the vegetarian guest found herself, is a strategy that can backfire. Plausibly, the "right" message to be sent to non-vegetarians is one that increases the chances that as many of them as possible will give up meat or at least reduce their meat consumption. If people perceive vegetarianism as a position that allows for no exception, they are probably less likely to become vegetarian. A flexible moral position is more appealing than a rigid one that allows for no exceptions. It is more likely that people would be convinced to become flexible vegetarians — that is, that they abstain from eating meat with some exceptions — than to become rigid vegetarians, and being a flexible vegetarian is preferable, from a moral perspective, to being a carnivore.
So the vegetarian guest's eating meat when offered has probably shown the host that it is possible to be a (flexible) vegetarian and, at the same time, occasionally enjoy some meat without feeling guilty. This has certainly made (flexible) vegetarianism look more accessible and more appealing than it would have been if the guest had refused to eat meat. Granted, perhaps by eating meat only occasionally one would lose the right to call herself a "vegetarian," but this might not be all that important. What matters more is that a world with many people who eat meat only occasionally is far preferable to the world we currently live in where there are relatively few vegetarians and a vast majority of carnivores.