I don't think that premise is true. I think most people who eat meat have at least a vague idea of how animals suffer to become food. Most probably don't know the specifics, and few will want to watch the videos showing conditions and procedures in factory farming, but it's not the knowledge that fosters empathy for animals. Humans are really good at disconnecting conflicting ideas becauseconflict makes us uncomfortable. They will say they prefer that animals suffer as little as possible to become food (or leather or sugar or pharmaceuticals, etc) but most humans won't change their behavior to match that stated preference.

It's the same way we feel about sweatshops or slave labor or child labor or the general exploitation of workers. The vast majority of humans don't want other humans to suffer, and most humans are at least aware that a child died to bring them that chocolate bar. That doesn't stop people from buying chocolate or fast fashion or bacon cheeseburgers.