What is outrageous about poverty is not that others have more, it is that some do not have enough.

Frankfurt · 'Equality as a Moral Ideal' · 1987

When inequality outrages us, let us look at what actually outrages us: not that the rich have ten houses, but that the poor have no roof. It is the shortfall, not the gap, that speaks to our sense of justice.
Now equality and sufficiency are two distinct things: one can equalize by leveling down, making everyone equally destitute, without fixing anything; and one can meet everyone's needs while leaving large gaps above.
If it is the shortfall that counts, the right measure is not 'as much as others' but 'enough to lead a dignified life': above that threshold, the gap loses most of its moral weight.

Therefore So justice aims neither at perfect equality of shares nor at the sheer freedom of exchange, but at a floor: that no one falls below the threshold of the necessary, inequality above it mattering far less.

How far does this reasoning convince you?

Not at all

Entirely