Yes I think so it would be less strain on nature and environment
A lot of people here assume that the only reason for being a vegetarian is the "moral" aspect. As a vegetarian, and being close to many vegetarians, I can say that is not so. It is the disgust.
Its kinda like this: Some people don't mind eating cows and goats, but they find the idea of eating a dog or cat disgusting. They find the idea of eating human flesh even more disgusting. Which is irrational. To us vegetarians, we find ALL flesh disgusting. Its not the morality.
Well it is rational if you really have a preference in terms of taste. But, many people have no idea what cat or dog tastes like, but they are like "yuck" at the idea of eating dog or cat.
A couple of days back we were driving on the highway, looking for a motel. All of us were very hungry, and I was the only vegetarian in the car. We found a dead dog (hit by some vehicle) lying on the road with its flesh & blood all over the place. I commented, "Well there's your lunch". My wife (non-vegetarian) said, "well just because you don't eat non-veg, you dont have to say things like that!". I said, "Whats the problem? You love that stuff, right? If you can eat goat, then why not dog?". Grim silence.
They had goat biryani and chicken curry for lunch. Guess I will never understand.
The only real answer would be social convention.
I don't think I would start a steady diet of cats and dogs because I have been psychologically programmed not to thing of those species as food. If I ever try it I may even be so disgusted by the thought that it will effect my perception of the taste.
I have eaten horse and, apart from it tasting disgusting, I have no quams about it. But I do know that in other cultures horses are not considered as foodstuff. It is quite common to have social conventions against the consumption of certain animals and nearly all have one about consuming fellow humans.