I'm not an expert, but it seems to me the way CPI imputes the cost of housing and several other things is broken. It looks like most Americans have seen much more inflation in the cost of housing, healthcare and education than the CPI would have you believe.

It includes housing in the form of rent (imputed rent in case you own the house). OP was talking about housing as an investment (like stocks), which is not covered under CPI.

Inflation has moved from product prices to asset prices. Just look at the stock market.