The reason it hurts the middle class is that the size of their mortgages are the first to be affected by inflation, whereas their wages are among the last.
Mortgage holders are stakeholders in inflation, hoping for appreciating property prices.
Mortgage holders are stakeholders in inflation, hoping for appreciating property prices.
Consider the relative size of new mortgages to wages. Since asset prices are typically leveraged on wages (through mortgages), assets will inflate faster than wages (unless the interest rate is set to counteract this.)
But inflation is only beneficial to /new/ buyers if wages inflate faster than assets. Otherwise the relative debt of all mortgage holders increases over time.
Whether asset inflation is beneficial to a home owner is debatable, since all properties appreciate at the same rate. "Moving up" still means increasing the relative size of the mortgage.