Inflation isn't inherently bad for the poor. If you have debts and inflation is above the (fixed) interest rate on your debts, you're coming out ahead.
The downside of inflation is wages and cost of living adjustments often don't keep pace with inflation because government statistics are rigged to understate the real rate of inflation and many things aren't even indexed to inflation. For example, the minimum wage has been $7.15 an hour in the US for about 15 years. Wage growth not keeping pace with inflation is, as far as inflation hawks are concerned, a feature not a bug as it increases public support for inflation hawk policies.
The downside of inflation is wages and cost of living adjustments often don't keep pace with inflation because government statistics are rigged to understate the real rate of inflation and many things aren't even indexed to inflation. For example, the minimum wage has been $7.15 an hour in the US for about 15 years. Wage growth not keeping pace with inflation is, as far as inflation hawks are concerned, a feature not a bug as it increases public support for inflation hawk policies.