As Stalin said, "One death is a tragedy, but a million is a statistic."
This Psychology Today article discusses the dynamics in detail; excerpt:
"Mother Teresa once said, 'If I look at the mass I will never act.' When Stalin and Mother Teresa agree on a point, I sit up and pay attention. It turns out that the human tendency to turn away from mass suffering is well documented. Deborah Small and Paul Slovic have termed this phenomenon the collapse of compassion. It's not simply that as the number of victims goes up, people's sympathy levels off. No, when the numbers go up, the amount of sympathy people feel goes perversely down. And with it goes the willingness to donate money or time to help."
This has obvious implications for animal advocacy. Many vegans talk about how many billions and billions of animals are killed every year. But as the above article relates, this just numbs people.
Furthermore, in the face of unfathomable numbers, the one burger or chicken leg someone is going to eat that day seems negligible -- indeed, less than negligible.
Obviously, if we are going to create a world where all these animals aren't killed, we have to convince people not to eat animals. We need to be psychologically insightful in our efforts to do this, instead of repeating facts / stories that move us. Indeed, if something is meaningful to us as long-time vegans and activists, it is almost certainly not the best way to reach someone who currently eats meat.
Finally: we are not only looking to get people to stop eating animals. Rather, we need them to maintain that change, be a positive example of compassionate living, and to help advocate for the animals. In other words, we need to think strategically about our advocacy -- not just the immediate impact.
If we do this, change can grow exponentially!