Owning a house is just a hedge on your future costs (assuming you are not one of those people who use it as a forced savings account). When you have paid off the house your costs become very predictable. Sure you have a large assets sitting there doing very little, but you don't have to worry about the landlord suddenly increasing the rent, or you being forced to move at a bad time, etc. So as a home owner you have less risk of unpredictable costs and events in the future. The downside is that there is a cost-benefit for that reduced risk, which is the money in the home could have been doing something else, possibly earning you more money. And you have the added risk of having to pay for repairs or replacements to the house, whereas the landlord would normally be responsible. Since homes 'tend' (I use that word loosely) to track inflation, they make really crappy investments. If they aren't tracking inflation, you end up in bubble territory and 2008 happens all over again.
Note - this is just the financial aspect of owning. Many people, myself included, get a lot of joy of actually owning something and being able to do whatever I want to the property. And that is very valuable and is hard to put an actual price tag on.