Not an economist either, but I think I can explain that one. CPI is a single rate derived from the change of price in a bunch of goods (houses aren't actually included, as another person noted). A change in CPI tells you nothing about the change in price of a particular good in it; it only tells you how much more expensive those goods are if you bought all of them.
Just as an example, let's say milk and eggs are the only thing on the CPI, and they're both at $2. If milk goes up to $3 and eggs go down to $1, the CPI says there was 0% inflation (assuming they don't adjust for quantity consumed). So rent can go up a lot without affecting the CPI too much, as long as the cost of other goods goes down enough to offset that increase.
Here's a graph showing inflation of different goods between 1998 and 2018: https://realinvestmentadvice.com/wp-content/uploads/2019/04/... As you can see, a lot of "mandatory" things inflated a lot, but the increase in those costs is offset by the decrease in electronics prices.
The CPI is meant, afaik, to gauge the increase in the cost of living for the "average person". It's useful for driving fiscal policy, but it's not terribly useful to laymen, imo (and that includes myself).
Houses are included in asset inflation, I believe. Here's a chart showing asset inflation: https://realinvestmentadvice.com/wp-content/uploads/2019/04/...
Real wages are more interesting to laymen, I think. Those are effectively wages adjusted over time based on inflation from CPI. Using your housing example again, it doesn't really matter if a house cost $200k 20 years ago and costs $400k now, as long as wages doubled over the same period, all things equal. Inflation is fine (for the purposes of buying a house) as long as wages rise to match that increase.
The reason many people can't buy houses anymore is that real wages have fallen. https://en.wikipedia.org/wiki/Real_wages Wikipedia has some interesting info on that. In an ideal world, inflation decreases the purchasing power of a dollar, but your employer gives you more of them to compensate for that. That never happened for many people.