Houses go up in price exactly in keeping with inflation. I buy a house with 10% down[1] as a way of locking in the current price, to avoid my rent going up every six months, even if the initial payment is more than my rent[2].

Time passes. The price of everything doubles. If I had kept my down payment instead of buying the house, it would have grown into twice as many dollars, and still be worth the original amount in actual value. My house has also doubled in value. But I only paid for 10% of it with pre-inflation dollars (and since then I have paid the mortgage with dollars of decreasing value). I come out ahead in that scenario - my net worth has grown, even adjusting for inflation.

[1] Yes, I am ignoring the difficulty of scraping together the down payment.

[2] Yes, I am also ignoring the difficulty of having enough spare cash to make the payments the first year or two.