Calm and reflective, the Archbishop of Canterbury does not come across as a natural controversialist. Yet Rowan Williams has developed quite a knack for attracting criticism, whether for saying nothing when the country's most senior Anglican cleric might be expected to take a view – his long silence over the Occupy protest at St Paul's Cathedral and the church splits it exposed – or for statements from the pulpit that sail close to the wind of politics.

With his sermon at Canterbury Cathedral on Christmas Day, Dr Williams managed to whip up a new storm, appearing to suggest an equivalence between speculating bankers and urban rioters. In fact, what he said was not that bankers and rioters were equally bad – or equally misunderstood. He implied rather that they could be seen as two manifestations of a deeper malaise affecting British society, in which "bonds have been broken, trust abused and lost".

But the implied parallel was too seductive to be rejected just like that, what with the Occupy protesters still encamped in the City of London, a new season of generous bank bonuses at hand, and riot prosecutions still wending their way through the courts. That this is how Dr Williams's words were instantly interpreted shows that the issue – bankers versus rioters – is not going away.

Superficial parallels cannot be denied. Greedy, or profiteering, bankers ran up a bill through their irresponsibility that the public, and not those who speculated with other people's money, had – and still have – to pay. Similarly, it can be argued, the rioters took their cue from the values of a society that excluded them, stealing and destroying as they felt was their due – again leaving the public to pick up the tab.

That the bankers did not break the law and that the rioters did can be seen from a certain perspective as proof of how our values have been skewed. So long as your profiteering is ambitious enough, you are home and dry in your multi-million-pound mansion; if you loot a flat-screen TV and a pair of trainers, you are on your way to prison.

The mistake, however, is to conclude that the parallel either excuses or exculpates rioting. Many factors combined to produce this summer's social explosion – which began, let it not be forgotten, with the shooting by police of a man in Tottenham and their failure to envisage what could follow. There was opportunism in what happened, as well as ingrained deprivation. And while the police presence and tactics were woefully inadequate, it cannot be coincidence that three quarters of those charged already had criminal records. What has emerged is that a section – albeit a small section – of British society feels that it is not bound by the law; on those evenings in August they came out to play.

The fortunes amassed by – some of – the country's bankers are a separate problem, reflecting the go-getting culture that took hold through the 1990s and allowed personal and corporate responsibility to go by the board. That so many think it reasonable to bracket them with rioters illustrates the extent to which our sense of justice has been affronted. The remedy, though, cannot lie in the tougher enforcement of existing laws – which were not broken – but in a reappraisal of priorities and values that Parliament and people must agree together. This is starting to happen, though too slowly.

As so often, there is a higher truth and a more prosaic one. Not all bankers are greedy; not all rioters were poor (though all broke the law). But profiteering bankers and rioters are both, in their separate ways, malignant growths on our body politic, and in that sense, the Archbishop is right.