Rent goes up more than pay. Solvency = the belt must tighten. You decide to eat chicken instead of beef because it isn't inflating as fast and it's good enough. The basket adjusts to model your "preference change." Inflation went down! Your real income went up! Wow amazing!
In the short term, basket adjustments are lagged and modest in impact, but in the long term they are everything. CPI is a good model of consumer price inflation vs last year but a terrible model when compounded. This is before going down the chained CPI and hedonic adjustment tangents, which both reliably adjust CPI in the wrong direction. Funny how all the dubious methodology points in one direction, that of understating inflation.
Worse, the very focus on consumer prices itself is highly misleading. Assets and liabilities matter in an economy that has a middle class and isn't just hand-to-mouth serfs. When assets inflate and paychecks don't and the response is dissaving and debt, that's a problem too. The American Dream isn't to Owner's Imputed Rent a house.