Why should the cost of home ownership and home renting be equal in the long run? According to the person in this video (at about 10:10) from the economist, the evidence shows that long run cost of owning and renting homes are approximately same. 

The video itself tries to explain it in the minute before that person speaks about the evidence showing this, but I dont understand the explanation. 

The video says that this is because home buyers have to make mortgage payments which include interest and maintenance costs such as insurance, repairs and so on. 

But I still don't understand their explanation because when people rent they have to make rent payments forever and they never get the house. However, when people buy house they have to make mortgage payements maybe for 30-40 years and after that the home is theirs and now they only need to make the upkeep cost which I always thought are small (but I am not a home owner so I dont know that for sure). So how come the evidence shows that they are roughly equal? Or is the video incorrect?
Note that the "cost of home ownership" depends not only on the house and the market, but also the individual. For someone who moves every year, home ownership is generally not a good option - that person incurs closing costs every year, and most of their mortgage payments at the start of the loan go to interest, rather than building a meaningful amount of equity in the house.  It would be far better for that person to simply rent, rather than throwing away a few percent of their home's value every year in closing costs.

With this in mind, it's possible that the characteristics of the population make renting and home ownership roughly equal in cost, when averaged over a long period of time and the entire population. If you're not going to stay in a home for several years, it will generally be more favorable to rent, since you do not have enough time to recoup up-front costs associated with buying. I don't have hard numbers to show this equivalence, but it's worth pointing out that annual cost of home ownership vs. renting has a component that is unrelated to market value or interest rate - individual lifestyle choices play a role as well. Empirically, we might find that renting is the better financial option for about as many people as would be better off with home ownership.