Not all of it does. There are inequalities that are unobjectionable from a moral point of view. To give a crude example, if A is in prison for a rape or murder that he committed, and after receiving a proportionate sentence as the outcome of a fair trial, while B, who is guilty of no crime, retains her freedom to go about, this is an inequality between A and B but it is a just inequality. It may be objected that my example is not what people generally have in mind when discussing inequality; they are referring, rather, to social and economic inequalities. No worries, I can adapt the example. If A works hard at a job for 10 years while B, in the same job, takes life really easy, then - assuming no other significant differential between them than that A made the effort and B preferred not to - B has no grounds to complain of the fact that A's life now goes better than B's does because A has earned better rewards; B has no grounds for complaint even if he or she has come to think that the years of taking it easy were a mistake. Ditto if A and B are in different occupations and A tries hard while B doesn't. The resulting inequalities here are not unjust inequalities - at least so long as we suppose that people are responsible agents and answerable for what they do (and, in this post, I'm not going to question this supposition).
Some inequalities do, however, matter morally - they are unjust. A paradigm example would be severe inequalities in the lives of children that are due to the different economic situations of their parents. Children are not responsible for the economic advantages and disadvantages they are born to. It is a matter of luck and the luck isn't evened up by what is called equality of opportunity. How can it be just for one child to live in great hardship or deprivation and another not, merely because the parents to whom they were born have fared differently? How can it be just that, not only their lives as children, but their life chances subsequently, right down to their expected longevity, should depend on something they could have done nothing about? Much social and economic inequality is of this kind: not earned, whether positively or negatively, not deserved, but due to a lottery of birth.
If inequalities matter morally, however, that is why they do, because of being unjust in themselves, and this brings me to the crux of the present post. In the column here Heather Stewart argues that 'a decent standard of living for those at the bottom of the heap should be the mark of a decent society'. That's for sure. In support of the contention Stewart details some of the indices of inequality in Britain today. But then she writes the following:
Yet as the High Pay Commission report argues, such a gaping divide between rich and poor is corrosive: it undermines any sense of belonging, or community, or mutual responsibility.
I have nothing against the principle of community, but I think that appealing to it in this context is problematic. Either the inequalities that appear troubling are morally objectionable in themselves or they aren't. If they are, that is why we should want to do something about them; not because it will erode our sense of community. On the other hand, if they aren't morally objectionable, why should they be overriden in the name of community. Communities shouldn't place impositions upon individuals within them only because they're aimed at things perceived as divisive. This can easily become a formula for illiberal conformism or worse.
I should perhaps end by emphasizing that I do not think the extent of the inequalities in Britain and other advanced capitalist societies is justifiable as the result of differential effort. Not remotely.