Raising an animal for food is different from keeping a pet, because I need to feed my kids
Feeding your children is a real duty, and where meat truly is the only way to do it, almost no one would blame you. But the need is for food, not for animals in particular, and for most families with access to shops, children can be fed well on plants. The animal is the same animal whatever role we give it.
My first duty is to my children, and it comes before abstract concern for animals. Where I live, animal foods are available, filling and nutrient-dense, and they are what my family can reliably get and afford. In some places crops barely grow at all. The difference between a pet and a farm animal is the role each plays in meeting human needs, and keeping my children fed is the most basic need there is.
The duty is real. The step from it to meat is the part that needs support. A parent has to feed their children. That does not mean a parent has to feed them animals, unless nothing else will do the job.
Where nothing else will, the case is strong. Pastoral communities in arid regions, places where crops fail, households where meat is the only affordable source of key nutrients: these are real situations, and the standard definition of veganism already allows for them with its 'as far as is possible and practicable'. Nobody serious asks a herder in the Sahel to let their children go hungry.
That is not most people's position, including most people who make this argument. Anyone who can buy rice, lentils, beans, oats, peanuts and vegetables can feed a child well, and the major dietetic associations say well-planned vegan diets are suitable at every life stage, with B12 and some planning. Plant staples are also usually the cheapest food on the shelf. So for most families the real choice is not between meat and hungry children. It is between two ways of feeding them.
The companion-versus-food distinction has the same problem. Raising a pig for food rather than as a companion changes what we intend to do with it. It does not change what the pig can feel, or what happens to it at transport and slaughter. If the difference is meant to be moral, it has to come from genuine need. Where the need is genuine, it holds. Where food is available that doesn't require an animal to be killed, the need isn't there, and the distinction is only a label we chose.
Presenting two options as though they were the only ones available when further options exist. Also called a false dichotomy, or black-and-white thinking.
How it applies here: The arguer moves from 'I need to feed my kids' to 'so raising animals for food is justified', as if the only options were meat or hungry children. For anyone with access to plant staples, there is a third option: feeding the children well without animals. That option is never addressed.