Lennie loves small animals. He never gets angry with them while they are alive. His problem is that he kills them by holding them too hard or handling them too roughly. Because of the combination of his mental handicap and his great strength, he doesn't realize what he is doing to the poor animals until it is too late. He doesn't seem able to learn to be gentle enough, though his heart is in the right place.
Lennie is delighted to have the puppy, but he somehow bumps it too hard and it dies. This makes him sad at first, and he strokes the puppy in regret. However, he realizes that George will know he killed it and fears that, as a result, George won't let him have rabbits on the farm they dream of buying. Therefore, he gets angry. He directs the anger at the puppy, saying:
“God damn you ... Why do you got to get killed? You ain’t so little as mice.” He picked up the pup and hurled it from him. He turned his back on it.