I've always been impressed by vegetarians, because of their comfort in the moral convictions that keep cows alive and suffering for their dairy and children, but never dead for their meat (and an end to their suffering).
The thought-terminating cliche raises its head again.
There is nothing "ecologically" sound about keeping cows alive and burping on the cheapest feed available. This is not a criticism of your response, just pointing out that these kinds of cliches become culturally embedded after a certain amount of time, even if they do not reflect the reality.
I'm not disagreeing with you, I'm just saying that people have lots of different reasons for choosing to be vegetarian, and animal welfare isn't always their concern. I certainly recognize dairy has a large ecological impact (I live in Ireland after all; we're choking on dairy) but someone who eats dairy and beef probably has a greater impact than someone who eats dairy and plant-based foods.