Fixed rate mortgage payments are constant, but rents rise with inflation. If people expect high inflation, that may explain why rents look cheap compared to current mortgage payments on comparable residences.
But in the short term, there really shouldn't be such a big gap between renting and owning. That means that there isn't a global shortage of housing in the market, but distortions in the market because of external factors. Clearly, right now, a renter is better off waiting and putting the difference in the bank.
Holding assets is a good hedge against inflation.
That and your mortgage is locked so your payment gets super cheap in high inflation situations.