I actually did a whole class on this and really researched the subject. It is a government policy and a gov't catch-phrase propagated by the woman's federation group (which is part of the party). They haven't really kept it a secret. It came out of a gov't policy that the quality of marriage was dropping in China as women were becoming more educated and what-not. And even though the rate of single women in their 30's is very low in China (it's about 25% in America, close to 50% in the UK but near 9% in China) the gov't realized they problem with the huge population disparity to begin with and they don't want it to grow cause they gotta look out for #1 (men).
Although the good news is that the women's federation has finally recently decided to stop using the word "leftover women" as they got a lot of push back from the (mostly educated) women and so they are not saying it anymore though the idea has gotten ahold in society. And they are still propagating the idea of less education is a good thing.
Also the "guys need a house before marriage" has now been proven to be a gov't propaganda policy to ensure the booming house market. And the interesting thing is the gov't has not addressed it towards young people, who might be savvy enough to see it, but they have been steadily feeding it to the older generation who then feels the pressure, and will do anything for their kids. There are some really interesting articles about that, with statistics and such about how it has been incredibly effective with the older generation.