It bothers us because we know that dogs are relatively intelligent, often kind, feel pain and get sad. In many ways they act like children. We know this because many of us have pets or know people who have dogs as pets. Same thing for horses, to a lesser degree. This makes it harder to lie to yourself or ignore their suffering, and makes us feel bad about eating meat and the suffering that inevitably entails. If pigs, who are surprisingly intelligent, were common household pets, we'd feel bad about that too. But they aren't, so we get to pretend that they're stupid and don't die in pain and in fear.
In many ways, it's not much different to how most of us decide to pretend that child labour or slavery no longer exist, despite regular revelations about the suffering our consumerist purchasing decisions perpetuate. Or how we're happy to buy unnecessary nonsense, replacing perfectly good clothes, replace a functional phone with the newest shiny thing, spend money on content that we could easily do without, rather than donate to a charity that could have prevented children and innocents dying needlessly. We know deep down that we're choosing to let people die, we pretend we don't so we can buy some more luxuries.
People are often evil. This is the baseline of human behaviour. We like to convince ourselves we're not, by occasional acts of goodness.