Well, hard to say. I'm technically considered a millenial and don't own a house though most of my friends do. Many of them bought before our market went insane. We're just coming out of a correction and some people who were idiotic and basically gambled with real estate lost a lot of money. Even now after the correction housing prices in my area are very high and the cost doesn't really reflect the quality of what you're getting. Part of the downside of the housing boom we had was that there were a lot of people investing in flipping houses so they were trying to do a quick turnover with shitty or low quality renovations that LOOK nice but won't last, so the price is artificially high.
Renting in my area is also unreasonable. I got into my place before the markets went up as well. They are renting smaller units for more money than I pay now and I have the largest unit in my block. I guess I got lucky there.
The type of house I'd want to live in long term that doesn't require a ridiculous amount of upgrades and that's in a decent neighbourhood will easily run over 600k. If I don't want to pay a bunch of mortgage insurance I have to have a 20% downpayment. That doesn't include about 10k or more in other fees that go along with buying a home like what we pay to the real estate agent, land transfer taxes, lawyer fees, etc. It's a LOT of money up front.
Would I like to own a house? Yes. Why? Because I want something of my own to treat how I choose over a very, very long period of time. I want something to build equity in over time. I want something that I can pay off before retiring. I want something that, when it comes time to downsize, I can sell for a profit. Obviously it wouldn't be my only investment but it would be a nice asset to have provided there's not a massive crash that never corrects.
At this time in my life home ownership is out of the question for the next few years.
Something else that's problematic with housing in my country is that there's a lot of money laundering that filters through real estate here. Right now there's a bit inquiry going on about that. We have so many FUCKING CONDOS that have absurd condo fees and no one lives in them because everyone wants an Air BnB business now. So if you buy a condo chances are your neighbours are all renting theirs out for a profit and you have no expectation that guests are going to shut the fuck up and not ruin everything.
At the end of the day I'm not sentimental about home ownership but I know a lot of people who are. If I find a good house at a good price in an area that I want to live in, great. If not, great. But I'll have to die in this house I currently rent otherwise because rents are skyrocketing right along with housing prices. I don't know what other people my age or younger plan to do but I don't think it will be buying a house without a significant contribution from their parents.