Most people believe that as house prices rise, this is good for home-owners. It seems obvious, that if you own something, and the price of that this rises, you become richer. You have made a profit.
But it is not true.
I cover the case where all houses increase uniformly. For example x → px where p>1 or x → x+Δx where Δx>0. Conversely if the price of your house is increasing while the prices of other houses are decreasing, you can indeed make a profit, and benefit from the price change.
When you buy something, then sell it for a higher price, you make a profit. But when you sell a house, you normally selling it to buy a most expensive house. So the profit is sunk into another asset. You can never obtain your profit in cash.
If the price of your house rises while you are living in it, then you sell it to buy a more expensive house (the usual case), then the price of the new house has also risen by at least as much. You would have been as well (or better) off if house prices has remained stable.
The people who can make money from housing inflation are people owning multiple houses, people who downsize, people who become homeless, the estates of people who die and have no children. Investment funds are the big beneficiary of housing inflation, because they are free to buy and sell all of their assets.
In fact if house prices were kept stable by progressive government policy (for example continuous adjustment of to mortgage term limits, loan-to-value limits, or property taxes, similar to what central banks do with interest rates) then investment funds would sell their housing stock in favour of more profitable assets. This would be an even greater benefit to society (including home owners) from stable house prices.
The biggest loser is of course first time buyers.
There are other effects. You could argue that governments benefit from increased taxes. Estate agents and solicitors benefit from higher fees.
The other winner is banks. The profit a bank makes from a mortgage is directly proportional to the price of the house. So banks benefit not from price changes but from maximising prices. (Banks benefit even more from high interest rates and long mortgage terms, at the expense of home-owners. But these factors also influence house-prices. So the above generally true but not a simple relationship).
The above is not a unique feature of the housing market. It is an example of inflation. As assets increase uniformly in value through inflation, it seems like asset holders are making profit. When you sell the asset you make more money, but money is useless unless you use it to buy another asset. The price of the new asset has also increased by the same amount. So the holder reaps no benefit from the increase. That's why economists say that the value of the asset remained the same but the value of money decreased.
So this result for the case of housing is not surprising. It is an example of inflation at work.
The main effect of housing inflation is a transfer of purchasing power (and in the long run, of money) from people buying and selling houses to banks and investment funds.