Do socio-biological determinants of health justify redistribution of wealth in grossly unequal societies?
Google "Low social status is bad for your health. Biologists are starting to understand why" to read an Economist article describing how relatively low social status acts as an epigenetic trigger, which can contribute to inflammation, heart disease, Alzheimer's, etc. In other words, relatively low social status makes you unhealthier, not just at the level of chronic stress and cortisol (see the work of Dr. Robert Sapolsky and the talk by Richard Wilkinson), but down to the level of your genes.
Consider also this idea by Robert Frank:
Namely, there are cases in which everyone pursuing their individual rational self interest leads to absurd or horrific outcomes, just as with the tragedy of the commons.
As primates, we are wired to seek and maintain high social status (for ourselves and our children.) If we fail to do so, arms race logic and our own epigenetic responses dictate that we will be worse off - you would be a sucker not to seek higher status, or to fail to give your children all the advantages (relative to other children) that you can, even if that means that kids who are smarter or more talented than your kids (impossible, I know, but humor me) don't get an equal shot.
See also this article describing how equality of outcome and equality of opportunity are essentially the same thing:
The government's role in the economy is to correct for such absurd outcomes, so that we can live and work more effectively together. In the 1950's we had a top marginal tax rate of 90%, yet today such talk is derided as "socialism," as though that's a bad thing. Given that relatively low social status has real negative (mental) health impacts upon people, how is it socially justified to have a country in which 25% of the income goes to 1% of the people?