economists rule the world

And so your teenage daughter is having sex

Actually that's not the reason.

It's pretty much that there are methods of preventing people from knowing this teenage daughter is having sex (contraception, etc), so she is at much higher rates than a century ago. However what's interesting, and something I keep having to point when it comes up in regards sex ed, is that higher incomes correlate more strongly with avoidance of sex (pre-marital) but also positively with the use of contraception (including condoms). This suggests a number of possible causes
1) That use of contraception, in particular condoms which are usually more accessible, decreases sexual activity. There's some case to be made here.
2) Knowledge of associated risk factors which encourage use of contraception (disease and pregnancy) also decrease sexual activity. I regard this is a slight but unlikely cause. Mostly because teenagers (along with everyone else) have notoriously bad ideas about their own mortality rates anyway. Giving them some high percentage chance of their contracting gonorrhea from a few minutes of awkward fumbling around each others genitalia doesn't seem likely to dissuade supercharged hormonal teens from having sex by itself, though it might give them a reason to find a condom at least.
3) That upper class kids are lying more than the lower class kids about their sexual activity, but not their use, knowledge, and access to contraception (or condoms). That's possible and it's not very easy to check. You can start by looking at the last statistic they cited: use of prostitutes. Upper class teenage men don't frequent them anymore than anyone else in that age bracket does, largely because of those aforementioned risk factors. It is possible that they are either 1) having less pre-marital teenage sex right alongside women or 2) having it, with the same quartile of women and one or both parties is lying about it (statistics for the pre-marital teenage sexuality of men were not cited on the page) or 3) having pre-marital sex within other quartiles of the female population. I exclude the possibility of higher levels of homosexual behavior on the part of either men or women in this group. I expect that would be fairly consistent over time, though it's possible it would or has increased. My guess is that the people doing the study did some regressions analysis on the data and found that the reported figure was rigorous enough to state as though it were factually representing what happens (that such young women were having less sex than their peers for some reason).
4) That there are other causal factors, such as family response to negative outcomes of a sexual act or a negative effect on a desired career/academic path, which are considered more effectively by upper class kids because of a modest cost-benefit analysis. There isn't as much of a benefit or cost visible to most lower class teens to abstinence or the use of contraception to prevent risks. I suppose it's also possible that there are groups of these young women who engage in sexual acts but not actual sexual intercourse and then parse their question response on this basis, on the knowledge that this will eliminate their likely exposure to the dreaded and usually more difficult problem of handling a teenage pregnancy but not their risk of sexually transmitted diseases. Some of which are easily treatable and some which are not at all.

Other than the last one, I'm not sure how this makes economists the problem. There are lots of thought experiment prone bodies of academia that sit around talking about things that nobody else considers polite conversation, such as teenage sexual activity. That last one only focuses on economics because of the "obsession" with incentives and self-interest within the economic field of study.

Seems like the demon spawn for parents is birth control and condoms which remove parental agency by reducing risk factors for their children to engage in sexual activity, not people like me who sit around contemplating sex ed policy from an economic perspective of costs and benefits to society. It also sounds like those same children can respond favorably to different incentives, such as a modest understanding of the positive and negative expectations of others unrelated to their private decisions to have sexual relationships more generally and specifically their active use of contraception to reduce the risks involved in those relations. If there are strong cultural or social negatives being communicated, such as "don't have sex because you'll have a kid and I will disown you and cut you off from the trust fund because you'll never get into college and will be a worthless single mom" along with lesser, more honest, and less offensive versions therein, then I'm guessing that will put a damper on the importance of losing one's virginity a lot more efficiently than lying to children about other dangers associated with their sexuality as many in the abstinence only crowd do concerning condoms for example (the net effect of which has been to reduce condom use mostly among lower income teens, with obvious results).

The most salient point of all of that was that there's little reason to worry about educating kids about condoms as though it will encourage sex. There are still plenty of (effective) ways parents or concerned citizens moralizing teenage sex can do that without distorting factual elements over birth control and STD transmission prevention. If all we were concerned about was condom use somehow encouraging more promiscuous sex, then what explains a larger number of teens who are more sexually active and yet less likely to use condoms as the backdrop against which this body of teens who are more likely to use condoms must be compared to state whether or not they are more sexually active?

As in all economic questions, the question becomes "compared to what?" Compared to 100 years ago, fine, condoms are making people more sexually active, assuming all else is equal. Compared to now, it doesn't look that way at all. In fact it's highly possible the reverse is true now. I'd suggest that means something other than the condoms is at fault for the effect of higher teenage sex now than 100 years ago.