From what I can tell, what is meant by "same" is that "both are something poor people do who aren't building wealth." It makes sense if you believe an important way to build wealth is to get a mortgage, stay in one place for a long time, and your residence is a big investment. It's an idea that makes sense if you were raised in a time where everyone believed housing could only go up.
For example, say I have 100k and am looking for a place to live. In one scenario I put 20% down on a 400k home, pay a bunch of closing costs and such. I'm left with a little leftover. I get a mortgage, build equity. Five or ten years alter I need to sell the house, but the value has fallen 20%. I pay more costs to get the place sold, and if I'm lucky, get 80-100k back.
Other scenario. I pay rent approximate to my mortgage. My 100k is invested, pretty conservatively, let's say it does 4% a year. At the end of the five years I have around 120k.
The renter has more money, and a lot more freedom when it comes time to move. This is kind of an oversimplification, but if we stopped subsidizing the first scenario (mortgage interest deduction, capital gains exeptions, etc) there would be even more scenarios where the renter builds a lot more wealth.