Consider a poor family spending about 90% of their income on day to day expenses; versus a rich family spending 20% of their income - if there's 10% inflation, the poor family will go from a 10% margin of survival to a 1% margin of survival, which is a 90% reduction of ability to survive or save. Vice the rich family which has only suffered a 2.5% decrease in this margin.
Let's say (and this is atypical, as I said, poor people are usually less in debt than rich people) the poor family is additionally 5% in debt, versus 0% as in the rich case. Do you think it's any consolation that the 5% debt is nominally valued (and therefore decreasing in real terms) in the face of the fact that the family now is spending 104% of their income on day to day expenses? Moreover, the way in which poor people use debt (very short-term loans) typically involves interest rates that are far too high to take advantage of real reduction in value, and are over far to short of a term even if they had reasonable interest rates.
Now obviously these numbers were chosen because they make the calculations easier; but you should consider plugging in values of your own and proving that it is general.