Women admit to cheating less than men, and this is reflected in a bias of studies whose methodology includes self-reporting. In general, women self-report about one third less sex partners than men. That presents a curious mathematical problem: who are all those extra men partnering with?
Let's say the average reported number of sex partners for males is 11.7 [1]. Now that means that the set of men has a number of connections into the set of women times 11.7. Say, the number of men in the set is 31M [2], then the number of connections is 362.7M. For the set of women, the numbers are 7.7, 32.2M, and 247.94M, respectively.
The connections can terminate in either of the sets, so we can have M-M, M-F, or F-F connections.
At one unlikely extreme, we could have no heterosexual (M-F) pairings at all, so that means 11.7 gay partners for men, and 7.7 lesbian partners for women. Clearly, this isn't the reality, not even in the UK. But even if we map all the connections from the female set to males, we'll end up with 247.94M hetero connections, no lesbian connections, and 114.76 connections from the male set onto itself, or 8.0 hetero + 3.7 gay connections per male, and 7.7 hetero + 0 lesbian connections per female.
There may be a large number of spinsters, and a small number of gay people may be skewing the mean away from the mode for the males, but the important take-away is that, mathematically, hetero-sexual partnerships always draw from both sets equally, and therefore the mean number of heterosex partners is always the same across the whole population.
[1] http://www.nhs.uk/news/2013/11November/Pages/Results-of-UK-S... [2] http://www.ons.gov.uk/ons/rel/census/2011-census/population-...
Uh, no, not from the sets under study. You've ignored time and space. The sets under study are the set of men and set of women currently living in a particular countries. The sets from whom their past partners are drawn (even assuming purely heterosexual relationships) may include people no longer living at the time of the survey, as well as people who are alive, but not living in the country under study (either at the time of the survey, or even ever.)
If you managed to get responses from representative sample of all men and women who had ever lived (which, you know, is logistically tricky), then you could validly argue that all heterosexual partnerships must draw evenly from both groups. But you don't, so you can't.
The imbalance could just be that UK men are more likely to have had past relationships with women not currently living in the UK than UK women are to have had with men not currently living in the UK. (It could also be the kind of reporting bias you suggest, and there are certainly other sociological reasons to suspect that such reporting bias is at least partially to blame -- its just not, even without bringing into it questions of same-sex pairings, the kind of mathematical necessity you make it out to be.)
Time. Women live longer on average, and there is also on average an age gap between heterosex partners (males older); therefore it is more probable that the male sex partner will be deceased, not the female. The numbers for females, if anything, should therefore be higher.
Space. If the UK is a net exporter of male sexual partners, that would mean that some other country or countries would be net importers. Regardless, the worldwide number of heterosex connections must be the same for women and men. But that's not the case. In every country, with the notable exception of New Zealand, women report less sex partners than men, and the worldwide aggregate for men is still unexplainedly higher than the aggregate for women.
Some studies suggest the gap to be due to women underreporting, some studies suggest prostitutes are underrepresented in the samples, but in the end, whenever somebody wants to argue that men tend to have more sex partners than women, let them know that (a) one number is pretty useless in telling the whole story, and (b) if conclusions of a study present a mathematical paradox, they should be taken with a grain of salt.
The simplest answer to your question ("who are all those extra men partnering with?") is incredibly simple: there's a smaller group of women who sleep with a greater number of men than vice-versa. And this makes total sense if you consider that women have more choice of partners, and men have less, and that there's a larger pool of men looking for purely physical/sexual relationships. Basically the availability of men is greater, the availability of women is smaller, and so the reported number of women cheating is smaller, and the reported number of men cheating is larger.
That's a falacy. If a small number of women raise the number of their sexual partners, the rest of the women must lower their number of sexual partners, to keep the average the same. That's not the way to explain the deficit.
I remember reading something that said something along the lines of "A married man in a bar, cheating, is more likely to do so without thought to the wedding ring - either oblivious to taking it off or apathetic".
Women doing the same thing were much more likely to make a conscious point of removing the wedding ring in the same situation.
But the 'why' is varied. It's illogical to say "they cheat because they are more likely to cheat". They cheat because of many factors, but according to surveys, they cheat more often out of a need for physical satisfaction, while women cheat more out of a need for emotional or intimate satisfaction.
As far as need for online services to help? That's completely dependent on the person, again. True, women get hit on more often & indiscriminately, so they'd have more choice. But they also can't necessarily get the emotional satisfaction they're looking for, so that narrows the field. Men just need to be attractive enough to get laid, which again definitely depends on the man.
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As a side rant: Assuming sex and gender were considered about the same, gender inequality is a function of gender differences. In other words, it's not only inevitable, it's normal. Women request [and should get] special care for breastfeeding/pumping, maternity leave, they have higher incidences of breast and ovarian cancer, they naturally have less muscle and are shorter on average, etc etc. These aren't controversial statements, and yet, they show simple examples of how women are different, and in some cases should be treated different in order to provide care. How would one make these differences "equal" among the genders? (obviously sex isn't gender, but clearly there's more cis-women than trans-women)