Dealing with heterosexual couplings only, the "50/50 balance = no excess singles" theory assumes men and women pair up equally, but if, say, a percentage of women go for a significantly smaller percentage of men - and share them - this would lead to an excess of single men.
As this seems to be a touchy subject with some, I'm not trying to make a point, just relating how this could statistically work - and of course, it would work the other way round and leave an excess of women.
This reversal may be indicated at the 50+ age ranges in some of the links where single women are in the excess in that demographic.