it's most likely because we understand that humans are capable of so much evil up to and including killing small animals just for fun, but when you view the deaths of animals, you realize how powerless they are against us and how they do not kill purely out of enjoyment like some humans do. I just felt sick inside from those three minutes.
To tell the truth, I've never really cried for any anime, evil some that were previously mentioned, but that ended when I saw Clannad After Story
parts that touched me most: (spoiler warnings
1. Nagisa's death
2. Ushio crying in Tomoya's arms
3. Tomoya telling his father he can finally rest
4. Ushio's death
Just about every time I watch those parts, I can't help but let a tear come out, though I never really break down, although I do die a little inside every time
But another thing that has come up recently is when Kajiura Ryuji and Muroto Hajime (the hobo hunters) in Gantz beat the man to death. It really hurt to see that because at that moment I can only imagine the cruelty of others