The concept of a psychopathic child makes people queasy. The two categories seem incompatible. Children, even badly behaved ones, are viewed as maintaining some fundamental innocence, whereas psychopaths are seen as fundamentally depraved. Neither stereotype is totally true. Children, just like adults, are capable of cruelty and violence, and even highly psychopathic people are not cruel or violent all of the time.

Psychopathy is a developmental disorder. It doesn’t emerge out of nowhere in adulthood – all psychopathic adults show signs during adolescence or childhood.

But this doesn’t mean we should label a child a psychopath – far from it. No responsible researcher or clinician ever would. Even though every adult psychopath began as a psychopathic child, the reverse is not true: many children with high psychopathy scores do not go on to become adult psychopaths. And remission can occur in response to favourable changes in a child’s environment, or as a result of innate developmental processes. But the fact that children can strongly express psychopathic traits should not be ignored.

What is sometimes overlooked is the impact on parents. During our research, the stories they told us about their children were heart-rending. Often they worried about what new episode of violence or theft or destructiveness each day would bring, about the safety of their other children and about their own safety.

In your mind the thought that “these kids must have really terrible parents” may be bouncing around. The belief that badly behaved children are the product of bad parenting is so deeply rooted in our culture that it is difficult to dispel. But let me try. I have talked to many families over the years and a common thread has been that the parents had tried literally every possible option before coming to see us – counsellors, medication, special schools, social workers. These were caring parents with resources. Nearly all had other children, none of whom were psychopathic.

Engaging in psychopathic behaviours seems to be driven by inherited factors, as we know from adoption and twin studies. These studies show that parenting and other environmental factors explain only a small fraction of the aggression of psychopathic children.

So what was going wrong with these children? Part of our research measured activity in the prefrontal cortex, right above the eyes, and a region called the amygdala. The amygdala (Latin for almond) is a lump of fat and fibre about half an inch in diameter that is buried beneath layers of cortex under each temple. Among other things, it plays a critical role in recognising fearful facial expressions.

The psychopathic children showed no activation – zero – in the righthand amygdala when they viewed the face of someone experiencing intense fear. The sight of another person in distress made no mark on this part of their brains. These children literally struggle to understand what they are looking at.

The children with psychopathic traits reported that they felt fear only infrequently and weakly. Two claimed they had never felt fear, whereas no healthy children said this. This suggested a possibility that amygdala dysfunction in psychopaths impairs not only their behaviour, but their fundamental ability to empathise with another’s fear.

If someone doesn’t understand what it means to feel fear, how can they empathise with it in others?

Good For Nothing: from Altruists to Psychopaths and Everyone in Between by Abigail Marsh (Robinson, £14.99) is available for £12.74 from bookshop.theguardian.com