Vegetarians claim a number of benefits from the practice. These are typically a combination of some of the following:
1. reduction of animal suffering 2. conservation of resources from removing inefficient meat production 3. health benefits
In some situations, such as a trip to a place like mongolia where most nutrition comes through meat, many of the values of vegetarianism can be preserved through a trade system - vegetarians could agree to have someone else, who lived in a more convenient area give up meat, and temporarily eat it while they were in Mongolia. The alternative would be to carry all their food with them, which would be a waste of energy, and may not work anyway.
Trading meat consumption would preserve the animal suffering & resource saving benefits. Depending on the nature of the health benefits (how long they take to 'set in'), it may even preserve these too.
Vegetarian can be considered a type of production - that is, they have decided to use their choices to influence the world. The supposed goal is just that - to influence the world to achieve goals, with the possibility of personal health goals on the side. This leads to the question of why vegetarians have decided that the most efficient way to meet their goals is on their own body; if they are interested in animal suffering or resource conservation, there are other, more efficient ways to meet those goals. For example, paying someone who lives near a farm to give up meat would reduce meat consumption by the same amount, and would also save all the transportation costs of the vegetables from the farm to the original vegetarian. This would achieve the alleged goals of the vegetarian more effectively. Or, if two meat-eaters offered to both become vegetarians if a vegetarian gives up the practice - what % of morality-based vegetarians would accept? I don't think many would, even if the trade could be guaranteed. There's a kind of personal ambivalence to eating meat, or personal benefits to being a vegetarian, which I think is the real reason behind it - although it's usually justified in global terms.
So instead of saying they are veg. because it's a personal challenge, or because they want to feel more pure, or they want to signal morality/health/purity, people talk about global benefits.
Vegetarians are now vulnerable to an anti-vegetarian strategy - meat-eaters can counteract their effects by simply eating all the meat the veg. gives up. Is this a real vulnerability? If it is, what's the point of being a vegetarian? I don't think it's as much of a weakness as you might think - every dollar the anti-vegetarian spends is a dollar he didn't use on some other purpose. And since spending money is equivalent to making people do things, using up resources, that is a savings. This only works if the damage from each dollar spent is equal - all externalities have to be accounted for.