YP: I can’t speak for 60 year olds, but through my parents, I know of many 55 year old older singles. (Ironically enough, they are all men, and to be fair, I can see why they’re still single.)
A factor may be that there’s now more of a “yeshivish system” as opposed to back then when there was somewhat less of a whole process in shidduchim. Also less (MUCH less) kollel.
As far as Mr Rechnitz’s whole statistics thing, that’s what really got my family roiled up. It seemed dangerously like pulling statistics out of a hat- it’s impossible to say how many people “will never get married”- it’s pure extrapolation (of dubious statistics in the first place) when really each person is different and there is no way of knowing.
Take one Bais Yaakov high school class. By Mr Rechnitz’s magical cut-off date of 25, only 70% of the class was married. By the time they hit their 25th reunion, there was a 100% marriage success rate (actually, 110%, but that’s not the point).
Shooting out numbers like that is a self-fulfilling prophecy. It only resigns people to their bad-as-death fate without cause. (The whole “bad-as-death” thing is another problem, but I’m late for work so I’ll leave it for now.)