I'm not convinced the personality thing is sufficient, or maybe I don't quite understand what you mean by that. Cows used to have names, like horses or dogs did. In contrast, house cats usually didn't.
Plus, the children used to play with the goats and sheep while they were still small. I'm not very familiar with the cows (my grandparents didn't have any), but I know that goats also tend to be fairly smart, curious and quite playful. As a kid it's fairly easy to develop some attachment to them, especially since there isn't that big of a size difference (a cow can be intimidating to a child because of its size).
You are probably right, it's not that simple. Probably many things need to come together for a specific output but I still think that it affects how you think about it and maybe in some cases can make you a nihilist for example. Humans are complex.
There's also different breed of cow, goat, and sheep used for meat vs wool. The meat breeds are much stupider and less personable. I could never kill one of my milk goats for meat, but my meat rabbits are a rather easy task.
Plus, the children used to play with the goats and sheep while they were still small. I'm not very familiar with the cows (my grandparents didn't have any), but I know that goats also tend to be fairly smart, curious and quite playful. As a kid it's fairly easy to develop some attachment to them, especially since there isn't that big of a size difference (a cow can be intimidating to a child because of its size).