Curiosity or exploration (i.e., the animal is injured or killed in the process of being examined, usually by a young or developmentally delayed child).
Peer pressure (peers may encourage animal abuse or require it as a part of an initiation rite).
Mood enhancement (to relieve boredom or depression).
Sexual gratification.
Forced abuse (the child is coerced into animal abuse by a more powerful individual).
Attachment to an animal (the child kills an animal to prevent its torture by another individual).
Animal phobias (that cause a pre-emptive attack on a feared animal).
Identification with the child's abuser (a victimized child may try to regain a sense of power by victimizing a more vulnerable animal).
Post-traumatic play (re-enacting violent episodes with an animal victim).
Imitation (copying a parent's or other adult's abusive "discipline" of animals).
Self-injury (using an animal to inflict injuries on the child's own body).
Rehearsal for interpersonal violence ("practicing" violence on stray animals or pets before engaging in violent acts against other people).
Vehicle for emotional abuse (injuring a sibling's pet to frighten the sibling).
Possible motivations for adults who abuse animals:
To control an animal (animal abuse as discipline or "training").
To retaliate against an animal.
To satisfy a prejudice against a species or breed.
To express aggression through an animal (training an animal to attack, using inflicted pain to create a "mean" dog).
To enhance one's own aggressiveness (such as using an animal victim for target practice).
To shock people for amusement.
To retaliate against other people (by hurting their pets or abusing animals in their presence).
To displace hostility from a person to an animal (attacking a vulnerable animal when assaulting the real human target is judged too risky).
To experience nonspecific sadism (enjoying the suffering experienced by the animal victim, in and of itself).
Source: "Animal Abuse and Youth Violence" — Frank Ascione, Ph.D., professor of Psychology at Utah State University.