Where are you getting this? To me it looks like household size dropped precipitously between 1947 and 1990, and then stabilized around 2.6 in 1990, and now it's around 2.5. I think rent has gone up a little more than 4% since 1990 though.
I actually would guess that you're probably right about an increase in single people or couples or empty nesters as compared with big families, but that it's been offset by a rise in young or semi-young adults living with roommates. That's just me guessing though.