Rent vs buy really depends (1) what's your down payment and (2) how long you're going to stay in your house.
If you have a high downpayment, and in the extreme case buy your house in cash, you don't have to pay any interest. You can take into account the revenue you could have got from your capital, but nowadays you can't get much without taking pretty big risks.
Then there's the long term. If you end up staying 30 years in the same house, buying is cheaper. Depending on your local market, the number of years you need to stay in house to make up for the purchasing fees (interests, taxes, etc.) is different. It's this number you need to find out. Of course when the real estate price was going up fast, the increase in value made it up pretty quickly so buying was an easy choice. That's no longer the case, you need to do the math.
So it's not whether it's universally better to buy or rent. It all depends on your local market, your downpayment, and how long you're willing to stay in your new house.
Discussions about "rent vs buy", and the corollary of "mortgage vs cash", rarely address the problem of you MUST make that payment every month. Pay up or lose it.
The notion of paying every month, pretty much for life, is deeply ingrained in society to the point of not renting/mortgaging seems downright weird. (It's kinda like the recurring threads where living on $1/meal is met with outrage by most, despite many doing so with great satisfaction.) Few start out with a primary goal being owning home & property outright ASAP. This normalizes the dependency factor, reinforcing a social dynamic where people can't take long vacations or high risks, and live in fear of financial devastation from sudden unemployment or disability, precisely because that massive monthly payment ever looms.
The normalization of rent/mortgage also means social expectation of costlier dwellings. Where our culture(s) were satisfied by much humbler abodes a few decades ago, we've now grown to expect vast variants on the McMansion theme as a minimum - shocked at any suggestion that buying a brick shoebox (which our [grand]parents were content with) outright might be financially sensible. I expect downvotes based on "you can't expect anyone to live in that! cash purchase of real estate is absurd unless you're rich!" Well yeah, if you insist on buying multi-thousand-square-foot floorspace in quasi-urban settings with lots of options, sure it's gonna cost ... but you can choose to live somewhere less expensive, in a smaller space, and own outright much sooner - giving you the freedom to take a sabbatical, or risk investments, or not worry about layoffs.
In retrospect, and stuck with a large mortgage (bought at the peak), I strongly suggest anyone entering the housing market focus on hoarding cash until they can buy something, anything, outright. The freedom full ownership bestows is remarkable. Pity society sneers at it.
This seems to miss a large percentage of the population which live in mega-citys. People arn't putting out a million dollars for "McMansions". A million dollars buys you an 800 sq ft 1 bed 1 bath condo. We are accepting the "brick shoebox", and we are paying through the nose for it.
Edit: And, at least for me, moving far away where its cheaper is not an option. My children will know their grandparents, and not because they make a 4 hour drive each way once a month or some such.
Oh, I'm not missing that scenario. My point still applies in full. Too expensive is too expensive, not just in cost but in risk and lost opportunity. Better maybe to talk the extended family into moving somewhere far less costly.
It's been said a few times in this thread, but you have to remember to make this calculation on equivalent properties. In a perfectly functioning market, there'd be no difference between "rental" inventory and "owner-occupied" inventory, but in practice there are often qualitative differences between the two, and if you value certain characteristics you will likely have to buy.
EDIT: Also, don't forget to change the "marginal tax rate" option under "Advanced Settings...Other..." Mortgage interest deductibility is (rightly or, as I think, wrongly) a substantial ownership subsidy, particularly for high-earners.
To add to your point, I live in a suburb/city that effectively bans rentals by making property taxes extremely expensive if the property is not both owner-occupied and a primary residence (homestead taxes). This is coupled with widespread HOA agreements that explicitly ban renting/subletting to not-close-relatives. The unsurprising effect is that higher income families live here and the cost of running the schools is consequently low. There are some other suburbs, but in that case you're committed to private schooling of your kids.
If you have a high downpayment, and in the extreme case buy your house in cash, you don't have to pay any interest. You can take into account the revenue you could have got from your capital, but nowadays you can't get much without taking pretty big risks.
Then there's the long term. If you end up staying 30 years in the same house, buying is cheaper. Depending on your local market, the number of years you need to stay in house to make up for the purchasing fees (interests, taxes, etc.) is different. It's this number you need to find out. Of course when the real estate price was going up fast, the increase in value made it up pretty quickly so buying was an easy choice. That's no longer the case, you need to do the math.
So it's not whether it's universally better to buy or rent. It all depends on your local market, your downpayment, and how long you're willing to stay in your new house.