The first words I say in The Ascent of Woman are: “There has never been a better time to have been born a woman.” I believe this to be true in aggregate and in particular for women in America. By every measurement we are either gaining on or are ahead of men. Since 2011 women have made up half the American workforce and the majority of the country’s graduates. But if we are getting our cake at last, guess what: we aren’t eating it, too.

When I was growing up, the message was that girls can do anything that boys can — and probably better. I don’t think it was meant to be a prophecy but it’s rather turned out that way. In America today the average undergraduate ratio is 57% women to 43% men. That’s the average, mind you. In some places it’s even worse. At Sarah Lawrence College, where I was a student, it’s more like 70-30.

Outside universities the gender gap isn’t much better. Among young adults with degrees there are five women for every four men. In some cities such as San Francisco, which is full of computer geeks and engineers, the imbalance is hardly noticeable. But others have turned into man deserts, especially for female graduates between the ages of 25 and 34.

Fort Lauderdale in Florida is the worst. If you are young, female and single, do not even think of taking a job there: it has 71% more women graduates than men. New York isn’t quite as bad but the figure is still terrible at 38% which is why, when you add the fact that up to 12% of the city’s male population is gay, there are 230,000 more single graduate women than men.

Yet only 20 years ago the dating decathlon was entirely skewed in our favour. During my twenties, when I contemplated my single graduate state I could at least take comfort from the knowledge that there were 117 Toms, Dicks and Harrys for every 100 of me. The only catch, according to a Harvard-Yale study published in 1985, was that I had to marry before I was 30. If I failed, then the dating pool would dry up before my very eyes, leaving me with just a 20% chance of getting married. If I were still manless by the age of 40, then my chance of a white wedding (or any wedding) fell to 2.6%.

As a 1986 cover article for Newsweek put it: a single graduate woman over 40 was more likely to be killed by a terrorist than find a husband.

Then came the revelation that the Harvard-Yale study was flawed. Later it transpired that Newsweek’s “terrorist” claim was actually a joke that had badly misfired. So, for a few years at least, it seemed as though women had nothing to fear except the ticking of their biological clocks. How wrong we were. The tick-tick in our ears was the demographic timebomb that began in 1996 when more women began to graduate than men.

I know what you are probably asking: is it really so bad that women are becoming better educated than men? The answer is yes. Yes it is. Please don’t get me wrong. The problem isn’t women and education; it’s what happens when a small disparity morphs into a major imbalance.

Right now there are nearly 2m more female than male undergraduates in America. To understand what could lie in store for many of these women, let’s go back to our unhitched 40-year-old. Assuming she hasn’t totally given up on the idea, she’s now swimming in her shrinking pond with only 33 men for every 50 women. The odds of finding someone haven’t yet reached the level of lightning strikes and terrorists, but they’re close.

Nowadays, of course, having a man around the house isn’t the be-all and end-all that it once was. Leaving aside the romance question, the mechanics of raising a child alone have never been simpler. Being a single parent doesn’t automatically lead to poverty if you belong to the managerial class — a section of society that is now more than 50% female.

The problem isn’t that women can’t find fulfilment without a boyfriend or husband. Of course we can. Nor is this about women refusing to “marry down”: since 2005 about 21% of wives have higher degrees than their husbands and 38% outearn them. It’s more about the law of the jungle as it translates to the mating habits of the hairless ape.

Anthropologists talk about the operational sex ratio (OSR), which predicts how sex imbalances will affect social behaviour. When males vastly outnumber females, there’s more violence, social unrest and greater emphasis on monogamous relationships. But when women outnumber men: ah well, there’s the rub. Let’s just say it doesn’t lead to peace and social harmony — or happy marriages.

According to a book that’s taking America by storm called Date-onomics: How Dating Became a Lopsided Numbers Game by Jon Birger, the current “mancession” enables men to behave like sexual predators without the usual social consequences.

The rot starts in college, where the recent increase in sexual assaults on campus has provoked a White House-led investigation. But it really sets in afterwards, aided by dating apps such as Tinder, Hinge and OKCupid, that have made the casual hook-up easier than ordering pizza.

Hook-up culture has a veneer of egalitarianism that gives it a kind of social legitimacy. But, as a recent article in Vanity Fair argued, it is aiding rampant sexism. What works a little for women — the ability to sleep with someone without too much hassle — is working a whole lot better for men. Being a scarce commodity they can up their price, demanding sex on their own terms while giving nothing back.

Women are turning to apps such as Tinder — Tinderellas they’re called — because there are so few alternatives to meeting single men. But then they find themselves having to navigate a sex market that treats them like sellers.

The irony is killing. The under-35s are outperforming men on every level and yet it is leading to even greater male exploitation of female sexuality. Birger aims his advice at women. His suggestions include: try going after men in the suburbs (they’re less spoilt for choice) and move to a different city. Mine is aimed at men: just remember, the woman you disrespected today could be your boss tomorrow.