Then there's the question of the relative value of animals' lives, which is relevant to dog owners - by 'humanely' killing your own pet you could (possibly*) prevent the far less humane slaughter of goodness knows how many chickens, lambs, whatever.
* Though you have to take into account whether the dog's food is made of the parts of a domestic animal that humans wouldn't eat, and also that you wouldn't actually save their lives, you'd just prevent them being born.
I have thought about this subject from before the age of 10, when my uncle had a turkey farm and I made myself follow him round to observe a turkey go all the way from gobbling to... being gobbled
I also have a degree in philosophy.... and still, the best justification I can give is that it 'feels' right to me and I feel uncomfortable eating meat. I will make the odd exception, e.g. if we're out for a meal and I really don't like the look of the veggie options, because I'm aware of all the contradictions in the arguments.
Possibly, the most effective way to lead a more ethical life is not to have children. However much meat you eat, or however many animals die to grow your veggies, it will be nothing compared to what your children, and your children's children, and their children, would have eaten.