I think most people want to be kind to animals and the main point we disagree on is whether it's cruel to kill them in a humane manner.
Meat eaters would say as long as the animal has been well treated and you kill them humanely so they are not scared or hurt then it's ok since the animal has benefited as it probably wouldn't even have lived at all if we hadn't bred it. It still had a good life, if shorter than natural. It didn't suffer and doesn't really know anything about its death.
Vegetarians or vegans either disagree that the killing can be done humanely enough or they think it's bad in itself to deprive the animal of life. Also some vegans think it's impossible to keep animals in kind enough conditions on farms or at least they can't afford to buy the very high welfare animal products. Some people who are otherwise vegan will eat eggs they produce at home, for example, as they know the chickens were well cared for but would not trust anyone they didn't know really well.
Personally as a meat eater I believe that the benefits in continued existence of their species and having a good life, are worth it for farm animals that are well treated and humanely killed. I don't want a countryside without sheep or cows and I do think they enjoy their lives if well treated. But I can fully understand why someone might not agree especially if they think the truly higher welfare products are too hard to get hold of. I do agree a lot of agriculture can be very cruel. I can see why they might think it's just wrong to kill an animal altogether too and that's the main question we have to decide on, as I said. Is it just wrong to kill at all? However I think this is too hard a question for little dc.
So if young dc asked I wouldn't want to talk about killing but I would say mummy thinks some farmers are cruel to animals and doesn't want to eat (or prepare) meat ever just in case an animal would be hurt, but Daddy thinks it's ok as long as you check the farmers are kind, but we all agree you must be kind to animals. Once the dc get a bit older you can each explain your point of view in more detail and see what they think.
We do live in a society of meat eaters and you don't want dc to think they are all horrible, so even if all the family were vegan it's important to explain that most people love animals but think it's ok to keep them on farms but you respectfully disagree with their point of view.
As they get older you could introduce the fact that some people don't really look into the cruel conditions animals can be kept in and show how even if they grow up to eat meat like their father they can make sure animals are treated kindly on farms by being aware of farming practices and only buying high welfare meat or animal products.