Britain needs an urgent debate about fairness – the responsibilities we all have to the wider society we live in, and to the taxpayer. Last week saw examples of extraordinary duplicity and criminal irresponsibility from both the upper and lower echelons of society.

Britain's most infamous benefits claimant, Mick Philpott, was jailed for life for the death of six of his 17 children in a fire he started. The case prompted a sometimes unedifying debate about the part played by our welfare system in the appalling events, amid claims that taxpayers had funded the chaotic lifestyles that nurtured tragedy. Meanwhile, a parliamentary inquiry into HBOS and a special report into Barclays commissioned by the bank itself exposed cavalier irresponsibility with others' savings in the quest for personal gain, with the taxpayer directly or indirectly picking up the pieces once disaster struck.

But instead of national conversations about encouraging fairness and responsibility at both the top and bottom of society, there has been a single-minded focus on the failings of those on the lower rungs of the ladder, often reinforced by an unwillingness to correct widespread misconceptions about the true levels of welfare payments. Philpott has become part of an unpleasant syllogism, shamelessly created by the beleaguered chancellor, George Osborne, in his efforts to portray the coalition's welfare "reforms" as grounded in morality and fairness.

Philpott, runs the argument, was party to the manslaughter of his children. He was also a benefit claimant who bred children as sources of income provided by an unreformed welfare state. Therefore, both the benefit system and its claimants are as morally corrupt as Philpott and the coalition's decision to reshape welfare, notably capping claimants' income at £26,000, is wise and in tune with the people's instincts.

The best that can be said about Mr Osborne's position, supported by the prime minister, is that he expresses a very partial truth supported by a moral position on fairness that is selective and discriminatory in its application. The worst is that it is a mendacious stigmatisation of a system that is all that stands between the majority of claimants and destitution. Yet to win this argument, defenders of the very principle of welfare, social security and the social contract that stands behind them have to ensure that what they are defending corresponds to fairness, thus revealing the mendacity and cruelty of Osborne's position. This they have failed to do, not least because the system has been allowed to drift too far away from fairness principles.

For the Tories strike a popular chord when they say they want an end to the something-for-nothing society and that welfare as it is currently organised rewards Philpott-style irresponsibility. One of the principles of fairness is that there should be a proportional relationship between what one contributes and what one gets back. This is an elemental human instinct, which Osborne invokes, and which the current welfare system insufficiently respects. William Beveridge, the architect of the welfare state, wanted to defend it from Osborne-type attacks by insisting it be based on the contribution principle. It would genuinely be a collective insurance system, with insurance premiums leading to proportional benefits – one's pension, unemployment and sickness benefits.

But successive governments have failed to earmark national insurance contributions for a dedicated fund that will pay out to beneficiaries on the basis of how much they have paid in. Instead, contributions have been treated as if they are income tax payments. This means that all benefits are funded out of general revenues at the discretion of the government of the day. How welfare is paid for has become a technical matter.

Indeed, Mr Osborne has investigated whether there is a case for merging tax and national insurance. But benefits that are part of a social insurance system that represents a social contract are not the same as benefits paid for from general taxation. The charge against the Conservatives is that they have no interest in expressing fairness as part of a social contract. Rather, they want a minimal system that addresses only acute need that they judge to be deserving, funded by taxation and at the discretion of politicians and officials.

This lack of concern with fairness extends to how we address the role of luck in our lives. If someone has an accident, people understand that it is fair to lend a helping hand. Philpott's children did nothing to deserve the fate of having him as their father. Indeed, no child has done anything to deserve living in a disadvantaged family. This is why society tries to relieve their circumstances by giving their parents the cash to feed, clothe and house them and why it tries to ensure they are properly parented and educated.

This is a cardinal fairness principle. The policy of capping total payments to families, and reducing their housing benefit if they are alleged to have too much space in their homes, in effect penalises children for the bad luck of being born to the wrong parents. Yes, Philpott abused the system, but we should not distort the life chances of hundreds of thousands of other disadvantaged children for one case.

Fairness principles are indivisible: the same must apply at the top of our society as it does at the bottom. HBOS was an insolvent bank and, as the parliamentary report makes clear, was managed disgracefully in the run-up to its collapse and takeover by Lloyds Bank, which in turn only survived because of a huge capital injection by the taxpayer. It is crystal clear that in the years before 2008, banks in general, and HBOS and RBS in particular, ran themselves with too little capital in order to maximise profits and bonuses. They were bailed out by the state providing both capital and more than £1tn of extra liquidity. How bankers are paid and how they run their banks have as profound an impact on society – and taxpayers – as the welfare system.

Yet Mr Osborne, the self-appointed champion of fairness, has fought tooth and nail against the European parliament's proposal to limit bankers' bonuses to twice their salaries. The proposal to ringfence commercial and investment banking, and raise banks' capital, will only be implemented in 2019, while public services are taking significant cuts now. The executives at the helm of HBOS whose actions cost billions of pounds directly – and indirectly contributed to our five-year recession – have suffered little more than reproach and personal embarrassment. More widely, 300,000 individuals with incomes over £150,000 are to enjoy a reduction in income tax from this weekend.

This is not a moment for a witch-hunt over welfare abusers. Rather, we need a proper argument about whether British society as a whole is fair. It is not one that Mr Osborne, or his policies, would win.