In this, the monthly analysis of the CPI report, the Inflation Guy homes in on a couple of reasons that core inflation is staying high, despite widespread forecasts that it should be decelerating more quickly:

Rents are still rising at about 6% per year, even though many economists have convinced themselves that rents should decline (despite higher costs for landlords, higher incomes for customers, and higher prices of a substitute), and
Wages are still rising at about 6% per year, which tends to lend persistence to core services ex-rents (so-called "Supercore").

There are some positive signs in the data, but even as inflation declines slowly on base effects there are few signs that core inflation is dropping below the 5% or so level it has been around for the last few years. A Fed on hold seems appropriate.

Reference: "How Much Do Labor Costs Drive Inflation", Economic Letter, San Francisco Federal Reserve

Ep. 69: This Month’s CPI Report - Rents and Wages Aren’t Falling!