A national average (which is what an inflation rate is) can only do so much. It's going to include people who spend very different amounts on housing, probably not much like the situation where you live.

No, the "averages smear out details" problem is completely separate to the core accusation I made and much less interesting. My accusation -- which you completely failed to address -- is that CPI systematically fails to account for forced substitution, introducing a systematic downwards bias that forces "real" incomes to rise over the long term as a direct result of the solvency constraint on individuals rather than improved access to goods and services in the economy.