The bare facts of the Copenhagen killings are not in dispute. But the reasons why a European capital and its citizens have again fallen victim to a merciless act of extreme Islamist violence are less easy to fathom, and certainly more contentious.



Already the shockwaves are spreading outwards, like a poison cloud carrying hate to the furthest reaches of a frightened and bewildered continent.



It seems clear the gunman was no professional. He fired at random into the crowd at the Krudttønden cafe. He failed to get inside the building and casualties were relatively few. Fleeing the scene, he hired a taxi home, which is how police tracked him and shot him dead – but only after a second murder at Copenhagen’s main synagogue on Krystalgade.



Danish security officials suggest a possible link with the Islamic State terrorists in Syria and Iraq, but have so far produced no evidence. There will be speculation about connections with other groups, such as al-Qaida in the Arabian Peninsula. But it appears more likely that the unidentified killer, who police said was Danish-born, was acting on his own.

If so, there may be similarities with the Islamists who attacked Charlie Hebdo magazine and a Jewish supermarket in Paris last month. The Kouachi brothers, perpetrators of the Hebdo attack, may have been trained by al-Qaida in Yemen, but this has never been confirmed.



What is certain is that they were “home-grown” jihadis who were radicalised during their formative years in Paris. Chérif Kouachi, for example, was enraged by the abusive treatment of Muslim prisoners at the US-run Abu Ghraib prison in Iraq.



The Copenhagen gunman may turn out to have a similar background, and likewise to have been a lone loose cannon. No terrorist group has claimed responsibility. But the febrile backdrop against which this individual’s crime took place is only too evident: a shooting war with Islamists across large swaths of the Muslim world, growing Islamophobia in western Europe, ever greater polarisation over Israel-Palestine – especially since last year’s Gaza conflict – and a linked rise in antisemitism.



All this mayhem and misery is reported and commented upon daily in Europe’s mass media and social media. The internet has become a noticeboard and recruiting ground for bigots of every type. Significantly, Danish police raided an internet cafe on Sunday that may have been used by the gunman.



The resulting unseen, online radicalisation of vulnerable, unbalanced or misguidedly idealistic young individuals is an intelligence nightmare. The security services have no persuasive answers. You cannot erect a roadblock or a firewall for ideas. Which is why attacks such as that in Copenhagen, even though the suspect was already known to police, seem impossible to prevent. And why more copycat attacks in Europe must be viewed as almost inevitable.



The Copenhagen fallout has to be contained somehow or a violent backlash could feed the existing crisis over how best to defend Europe’s cherished values of freedom of speech and religion.



David Cameron and Barack Obama lined up on Sunday to defend these values. They might be more usefully employed in acknowledging that many current problems can be traced back to the Anglo-American destabilisation of post-2003 Iraq and to the west’s connivance in the suppression of Arab spring pro-democracy uprisings.



In the short term, calls for increased security for frightened Jewish communities, including in Britain, are wholly understandable. Muslim communities deserve similar consideration. But the rash appeal by Binyamin Netanyahu, Israel’s prime minister, for all of Europe’s Jews to up sticks and emigrate to Israel is unhelpful. Running away is not the way to respond to intimidation. As one rabbi noted, to heed Netanyahu would be to give in to the terrorists.