Consider a hypothetical city with a population of 100,000:
1960: average household size: 3.63 persons
1960 housing units needed at 3.63 persons/household: 27,548 units
2020: average household size: 2.28 persons
2020 housing units needed at 2.28 persons/household: 43,860 units
So even with zero population growth, the city would need 59% more housing units.
That increase in demand drives up the price per housing unit.
At the same time, the decrease in the number of people per unit reduces each household's earning power, and makes it much more difficult for that household to afford the cost of housing.
No wonder few can afford to buy their own place.