We have a hard time making sense of people like Joanna Dennehy, who murdered Lukasz Slaboszewski, John Chapman and Kevin Lee, and attempted to murder Robin Bereza and John Rogers. Her male accomplices Gary Stretch and Leslie Layton were convicted at the Old Bailey today. A third accomplice, Robert Moore, had already pleaded guilty.

Women like Dennehy confuse us, unsettling our understandings of who women are and how they should behave. Contemporary notions of femininity do not go hand in hand with fatal violence, so we develop another way of making sense of them – the "mad" or "bad" dichotomy.

In the "bad" approach, we take away their identities as women, remodelling them as monsters. Dennehy has been portrayed as witch-like, "casting a spell" on her victims and accomplices – a witness's description of her in court as a "rattlesnake" brings to mind the serpents of myth and legend.

In the "mad" approach we explain behaviour away in a mental ill-health vacuum. We have heard about Dennehy's well-documented issues in this regard – she is a long-term abuser of drugs and alcohol, on arrest she was sectioned under the Mental Health Act, and psychiatric assessments found her to have psychopathic, antisocial and emotional instability disorders.

Creating monsters or crazed lunatics through the "bad" or "mad" labels are convenient ways of making sense of female multiple murderers like Dennehy. It helps us file them away and carry on with our lives, safe in the knowledge that they are not like the rest of us, they are smudges on an otherwise optimistic landscape in which police-recorded homicide rates have steeply declined in the last 10 years.

Granted, as a murderer, Dennehy is unusual, even when compared to the very small number of other women who have killed multiple times. This is a case where a complex interaction of social and psychological factors have ended in extreme events.

However, if we are to develop a more meaningful understanding of this type of crime, we need to resist the urge to dismiss her as a mad or bad aberration and look at the bigger picture in which fatal violence emerged. It is her disconnect from mainstream society that we need to focus our attention on.

Dennehy highlights the sharp end of what can happen when someone falls completely between the cracks in society. Our social institutions – family, religion, education, economy, polity – are the foundations on which we build our lives. They provide us with sets of values and principles, frameworks to make sense of our existence, blueprints for action in particular situations. While everyone's "institutional jigsaw" will be unique – family being more significant for some than economy, for instance – we all belong to society "through" them. Dennehy's life was whipped up into a chaotic tornado, blowing her away from all of the institutions that keep the rest of us on the straight and narrow.

She detached from the family altogether – both that into which she was born and that she created with her ex-partner. She was entirely disengaged from the economy, not making any paid or voluntary contribution. She dropped out of formal education in her mid-teens and there is no evidence of any realistic efforts to develop knowledge or skills that could enrich her life or those of others. She came to value nothing, believe in nothing, reject society and any contribution she could make to it – pursuing only her own increasingly bizarre impulses in an existence where the line between fantasy and reality had become increasingly blurred.

Contemporary society is characterised by an increasingly selfish and privatised culture of individualism in which we are all very good at "minding our own business". We look on as people like Dennehy disappear off the institutional radar, outside of the mainstream boundaries and structures, with no social filter on their behaviour, no one to say stop. Not all of these drifters will become murderers but they are highly likely to cause harm – either to themselves or other people. Unless we develop our collective sense of responsibility and willingness to challenge our own and other people's behaviour, this is likely to continue.

So instead of asking "why did she do it?" in the aftermath of the Dennehy case, we need to ask what was there to stop her. That will involve taking a good look at ourselves.