X hit the nail right on and drove it in all the way in one shot. Opinion and preferences are based on complex psychological interactions and should not be simply argued against.
On to the meat of the topic…
Arguments against meat are lame ethical stances based on opinion and no decent research. Any research touted as showning meat as bad has protein intake at 15% of calories tops, with wheat intake around 25% of total calories (80% of that wheat is refined), refined sugars at around 15% and refined vegetable oils at around 18%. And from these figures of average intakes, they try to find a correlation between long term health issues and a dietary survey that estimates intakes instead of meticulously recording intake.
These diets that are supposedly high meat are held up as cases of poor health which is obviously related to the poor micronutrient density of 50-60% of the diet which comes from empty calories. Most vegetarian diets are really breadatarian diets with the already low protein intake taken from different sources. The actual performance of these diets is worse than the standard western diet as macro and micronutrient intake does not change much.
Now there are some people who follow a balanced vegetarian diet and are able to get all the nutrients they require and them some, but this is a very small part of the population. This is usually also lacto-ovo-pesco styles as opposed to vegan.
As for people clinging to beliefs about diet, realize that this is a matter of faith, not science. Food and taboos surrounding it is one of the largest differentiators of cultural behavior. Often a person who is drawn to these beliefs and actions has had their emotions toyed with and those on the veggie side are some of the most heinous in using the same types of mind tricks and power moves previously used by cults and religions to control people.
I have known 3 people who were veggies. One a male friend was a vegan complaining of feeling like shit. I told him he needed meat. The best argument he had was economic. I sent him pictures of New Zealand cows and sheep grazing on mountains were no crop could be reasonably grown, yet meat production represented an environmentally sound and economically optimal resource extraction. When I saw him a few months later, he looked far healthier and had put on 20 pounds of muscle without lifting and was full of energy. Simply showing him that the worst case scenario was not representative of reality was enough to get him to stop feeling guilty about being a spoiled upper-middle class kid using vegetarianism as a social/status tool.
The second case is another male friend who has an inborn genetic condition that is exacerbated by certain amino acids. He is on a very carefully controlled and monitored diet that works for him. He eats animal protein as often as he can get away with, but it is almost never. I would never dream of trying to influence his intake.
The third is a female friend. I know that the reasons she has is somewhat similar to the first case, but she eats dairy and sometimes fish. Instead of launching the full press as I did with my male friend, I try to emphasize what she does well (dairy, vegetable, fruits, healthy fats) rather than what is wrong, because then she wouldn’t talk at all.
With such choices, it is important to realize that there is often a spiritual/yearning to follow a path to enlightenment component that if you cannot provide as part of your pro-meat rant, they will dismiss all you say even though they may agree with more than they disagree with. This combined with the psychological aspects of who may be influencing these ideas in the first place may allow you to see why a person is prone to following such a plan that seems to offer nothing to its adherents.