That might be true, but that argument overlooks one of the biggest reasons young people aren’t buying houses: Most of them simply don’t have enough money saved to clear the hurdle of a down payment. A mortgage might well be cheaper overall, but the one-time cost of becoming a homeowner is simply too high for most of them. While the job market is slowly getting better, Millennial wage growth remains pretty slow and student-debt loads continue to rise. On top of that, they’re expected to save up the little they can spare as they continue paying rent that’s only getting more expensive.

So what does the typical prospective homeowner’s choice actually look like? In August 2015, the median price of a home in the U.S. was around $292,000, which would require saving up nearly $30,000 for purchase. Additionally, it’s not like they’re going off to buy a house the moment they have $30,000 saved up—for example, financial wisdom suggests saving up to six months worth of expenses as an emergency fund. And that difficult proposition is based on the national median home price, but young people skew toward living in cities with steep home prices.

And then there’s the question of how excited Millennials are by the houses they have to choose from in the market. In Houston for instance, the median home price is $162,784 and the median cost to rent an apartment is $1,550. According to Trulia, buying in the Houston metro area is nearly 50 percent cheaper than renting, and in a city where all housing is comparably cheap, buying looks good. For the median price or less, Millennials there have the option of buying anything from a tiny apartment to a three-bedroom home—which is great.

But in plenty of other cities, homes that Millennials can afford to buy aren’t nearly as appealing as the places they can afford to rent. In New York, for instance, the median price of a home is listed as about $438,000. Buying there is 5 percent cheaper. But $438,000 won’t buy very much. In that price range many offerings are tiny studios and one bedrooms. Larger spaces—the kinds people buy when thinking about starting families or offering guests accommodations nicer than a couch—are much further away from city centers, requiring long, multi-vehicle commutes or buying a car. And a lot of more affordable properties are older, likely requiring upgrades or renovations that could make them pricier than they seem. The same is true of cities like D.C., San Francisco, and Los Angeles.

In some of the nation’s more expensive cities, saving up for a down payment would require more than $40,000, plus savings for a rainy day. Even if Millennials were able to scrape that together, all while paying their current rent, moving would still mean forgoing a favorable location, any building amenities they might have, and the freedom to move on short notice. It’s no wonder that, after making that calculation, more of them are picking renting over buying.