Children who kill fall into different categories, according to their traits, situations, and motivations.  Some kills are accidental, such as those involving kids who find their parents' guns, but many occur within a specific type of context and have motives.  Most of the experts categorize these killings by kids as:

Inner city or gang killers

These are kids who grow up in violent environments and who may have violent role models, such that their typical mode of response, whether for self-defense or just to get what they want, is violence.  This also includes gang killers, or children who are pressured from within a gang to kill.  They feel more powerful as a member of the gang, so they will do what it takes to get respect.  In fact, within some gangs any restraint on violence is viewed as weak.

Killing within a family

Kids who kill members of their family for reasons other than an accident, feel pressured by demands, abuse, hatred, desire for gain, and even by the need of other family members.  One 14-year-old enlisted this brother to help him murder their parents, and one mother provoked her son into killing his father. A fourteen-year-old in China killed his family because he thought his mother was not taking care of him properly.  When he was ill one night, she ordered him back to bed.  Instead, he stabbed his father 37 times, his mother 72 times and his grandmother 56 times.  Then he washed his hair and watched a videotape.

Cult killings

16-year-old Roderick Ferrell killed the parents of his former girlfriend in order to steal their car so he could take his friends, members of his vampire cult, to New Orleans.  A lot of kids identify themselves as Satanists because it gives them the feeling of power over others and the mystique of having secret associations with another world.  It also gives them license to do things like rob, damage property, and kill.  Sometimes they decide that human sacrifice is necessary to increase their powers, so they kill.  Ferrell claimed that he needed many victims in order to open the Gates of Hell.

Pathological Killings

Sam Manzie, 15, opened the door to eleven-year-old Eddie Werner, who was out raising money for his school.  He invited the boy in, then raped and strangled him, hiding Werner's body outside.  Manzie had been the victim of a child abuser and had shown signs of serious mental illness.  His parents had desperately tried to get him help and were convinced that he would become violent.  A doctor interviewed the boy for about ten minutes and told the parents to take him home.  They were over-reacting, he said.  Only three days later he murdered Werner.  Many people have a difficult time believing that children can be mentally ill, but they suffer depression and paranoid schizophrenia just like adults.  When it goes undiagnosed and untreated, it can spell trouble.

 School killers

They generally act on a perceived wrong done to them by others and view a climactic closure to the situation as the only way out.  Frustrations accumulate into rage that motivates a spree.  Michael Carneal, who shot into a prayer group in Paducah, Kentucky, was constantly baited by the other students.  They said he had "Michael germs" and stole his lunch. One day he had a gun and even then the other boys taunted him.  Finally he decided to act out and he ended up killing three students.6.    Killing committed during another crime: Fifteen-year-old Sandy Shaw lured James Kelly, 24, into the Nevada desert in 1986 so that she and two friends could rob him.  They needed money to post bail for Sandy's boyfriend.  They lifted $1400 and then shot him six times.  They even took friends out to see the body.

Sexual killings

James Pinkerton Kelly, 17, killed a neighbor.  First he sliced open her stomach and ejaculated into the wound.  Then he slit her throat and cut off her breasts.  Before he was arrested, he managed to do the same thing to another woman.
Hate crimes

Two boys, 17 and 14, shot a man in the head and then ran over him repeatedly with their car just because he was gay.  Such crimes begin with anger and hate and often involve a build-up of rage.  However, there are cases where the killings happened just so the killers could brag to their friends that they'd rid the world of such a person.

Kids who kill themselves

Five teenagers killed themselves in Goffstown, New Hampshire over a period of two years in the early 1990s.  Another kid, Jeremy Delle, went to school and blew his brains out in front of thirty other students.  Such kids tend to be lonely and depressed, but also want their self-violence to have painful reverberations in the lives of others.  Some of the school shooters were suicidal as well, and wanted to take others down with them.

Kids who kill their babies

In upstate New York, a fifteen-year-old girl gave birth to a baby.  She cleaned it up, wrapped it in a towel and plastic bag, and then tossed it down an eleven-foot embankment.  She was arrested and she told the police that her mother, who did not know that she was pregnant, would have gotten upset with her.  Quite often either the girl involved, or a couple, have done this to avoid parental disapproval or just to avoid having the responsibility of a child while they were children themselves.  Sometimes the girls claim postpartum depression.

From Wikipedia