"The reason he should do this does not come readily," David Wadman, the East Sussex coroner, said at an inquest into the deaths last week.
Yet the case is not as unusual as it might seem. Every six to eight weeks a man or a woman - usually a man - kills their partner or their children and then themself.
Ian Lazenby, from Humberside, killed his three daughters and himself after his wife left him because of his violence. In London, Jose Pimenta pushed his two young sons off a fourth-floor balcony and then jumped off after his estranged wife told him she had begun a new relationship. In Dorset, Mark Bradley killed himself and his two children in his fume-filled car after murdering their mother. She had told him she had had an affair and wanted a separation.
Dr Chris Milroy, a forensic pathologist at the University of Sheffield's medico-legal centre, who has made a study of these parent-child killings said: "Murder-suicide crosses socio-economic groups - we even had a coroner who killed his wife with a Waterford cut-glass decanter."
But nearly all the assailants are men. "Men are usually the perpetrators of violence, anyway, but it's higher with murder-suicide. The man usually kills his wife because there's been a breakdown in the relationship and he does it out of jealousy. When they kill children, it is usually revenge - 'If I can't have them, you can't have them'."
But there are other reasons. In some cases, the perpetrator is mentally ill, in others there are financial problems.
When women kill, Dr Milroy said, it is often because they feel that their children's lives have been destroyed. In December 1995, Elaine Smith drove into a river with her son Christopher, seven, and daughter Clare, three, strapped in the back of the car after her husband said he wanted a divorce and was going to spend Christmas with his lover.
Dr Milroy's interest in murder-suicide was provoked when he encountered three similar cases in a week.
Research showed the same phenomenon occurred elsewhere although in Australia, for instance, murder-suicide occurs twice as often.
One of the differences between British murder rates and the rest of the world's is the general absence of guns, Dr Milroy said.
With about 700 unlawful killings a year, it works out at 13 for every million of the population. The rate in America is 10 times that. Although Switzerland is generally law-abiding, for example, when people murder they use guns.
Yet 40 per cent of murder-suicides in Britain use guns compared with 10 per cent of murder cases overall. Curiously, although the murder rate in Britain has doubled since 1960, the number of people who commit suicide after killing has remained fairly constant.
Dr Milroy said it was difficult to say whether there was anything that could be done to prevent the murder-suicides.
Sarah Heatley, whose estranged husband killed their two children then himself, believes greater care should be taken in assessing whether men who show disturbed or violent tendencies should be given access to their children.
And Scottish women's groups lobbied last year for a special inclusion in the Children's Act barring fathers with a history of domestic abuse from unsupervised contact with their children pending an investigation.
But Dr Milroy said: "If there are 100,000 marriage breakups a year and seven men kill their children, how do you put that into the equation? How are you going to go about assessing every man to say whether they are dangerous or not?"
He added: "But you could argue that if it's a one in 600 million chance of contracting CJD from beef on the bone, the risk of a man killing his children is statistically higher."