How much of that is due to money though. I have a kid, live in an apartment in the city and shudder at the concept of moving the suburb. However if you want at least 3 bedrooms, a reasonably safe, kid-friendly neighborhood and access to good schools then you have to pay a lot of money, certainly more than I can reasonably afford with burying myself in way too much debt. Everybody I know (with one or two exceptions) who's moved to the suburbs has done so for largely financial reasons. Had prices in attractive areas in the city been lower they quite probably would have stayed.
I think that, similar to the way New Urbanism was viewed in the 1990's (no demand, so why build it), urban family living is a case where the demand appears as soon as the supply is present. But good luck getting a real estate developer on board when they can just stick to the tried and true of sucking in the yupsters. The closest thing you get to families in a lot of these place are BF/GF with a dog.
In Vancouver, families go into the burbs - whether or not this should be the case or what we can do to change this reality seems orthogonal to the main point: that rent increases are not impacting families as much as singles.
Also, keep in mind that Vancouver's urban core is really, really small - roughly 2.5 sq. mi by my estimation. In this core is the hub of the city's nightlife and a huge attraction for the bridge-and-tunnel crowd - not exactly the most family-friendly environment. There is a substantial lack of urbanism in Vancouver that is separated from the lifestyle of early-mid 20-somethings.