Inflation calculations doesn't include housing price.
I don’t know which calculations are you talking about precisely, but usually (US,EU,OECD) the hosing costs are included in the form of actaul rents, imputed rents, and maintenance costs.
Says who? They generally do.
The real lesson is statistics used in political discussion are ALWAYS manipulated into meaninglessness. If you can hear an axe grinding in the background you know the numbers are have been carefully and methodically rendered meaningless. The trick is to find statistics that aren't used (or aren't used as much) in political discussion. What is the ... divorce rate, or percentage of psychologically medicated people, or suicide rate, or addiction rate or average children per women, crime rates, immigration in or out of an area, job market trends by occupation and pay rate, ratio of local school academic spending to athletic spending, or similar non-headline metrics of success (or not success).