In terms of welfare (i.e., overall well-being), there is great inequality among dogs. Some, such as my niece's Tag, are utterly spoiled. They have the best food money can buy, climate-controlled shelter, comfortable bedding, ample exercise, liberty to move about, toys to play with, and medical care (including control of parasites). Some dogs have their basic needs satisfied, but little more. Some, sadly, do not have their basic needs satisfied. (This latter category includes those that are abused.) Should we be concerned with this inequality? I don't see why we should. What we should be concerned with is not the gap between "rich" dogs and "poor" dogs, but the absolute welfare level of dogs. No dog should have its basic needs unsatisfied. Think of it as creating a floor below which no dog is allowed to fall. Once we create this floor, who cares whether some dogs are above it? Who cares that some dogs are spoiled when every dog has a decent life? Do you see the distinction I'm drawing? Inequality per se is morally irrelevant. What's important is welfare.
Now let's focus on human beings. Does anything change? It seems to me that it doesn't. One difference between human beings and dogs is that human beings can see how others live, can measure the gap between their own resources and those of others, and can envy those who have more. But why should any of this matter? Should we base public policy on envy? If people who have their basic needs satisfied are pained at the sight (or thought) of others who have more than they need, they have a problem; but it's not a problem for which there is a public solution. In other words, it's not a matter of justice. You hear a lot these days about the "gap" between rich and poor, and about how the gap is increasing rather than decreasing. How many of the poor for whom crocodile tears are being shed have their basic needs unsatisfied? How many are suffering for lack of food, fuel, shelter, clothing, or medical care? If any of them are, then we should be concerned with that, not with (1) how far they are from others or (2) whether they're getting farther from others.
Progressives (i.e., egalitarians) are trying to shift the debate from welfare to equality, because they know that, as regards human beings, they have lost the welfare argument. The best sign of this is the obesity epidemic among those at lower income levels. Far from having too little food, they have too much!