The multiple ads question is interesting though, and might very well be a valid defense, since they then are advertising to both.
To briefly speak of ethical and legal issues, it is highly doubtful that they would have a policy of not hiring women if women actually apply for the position (and that would most certainly be illegal). Much more likely is that whoever ran the Facebook campaign checked off that option in an dumb attempt at controlling ad campaign costs? Or maybe they ran a separate campaign to recruit women? Or maybe some other non-nefarious reason.
Different audience segments may want different things from a job. For example, an increasing number of workplaces are offering paid paternity leave. Maybe that's something you want to specifically mention to men.
1) Is making a little economy really more important than giving equal opportunity ? 2) What makes you think you, or the person that designed the ad, knows best what might women (or any other group that might be discriminated against with similar practices) are interested in?
And that, especially when advertising for a job! Women may not be particularly "excited" by the message that conveys the ad, but they might be looking for a job all the same.
All your points sound the same to me, it comes down to : "women like cooking, teamwork and are not interested in being trucker, policemen or technologists, and men like sports and being stong and don't want to be a hairdresser or a nurse" now let's apply these hard facts to cut the costs when advertising for jobs. That way we make sure our stereotypes stay true, and it doesn't matter if it's unfair, it's just how are things. And I don't think I can change your strongly stereotypical view of gender in this comment alone, but I'm telling you : that can change, and women want that to change, because they want equal pay, and equal pay also means equal opportunity to high paying jobs.
Employment opportunity is not the ideal topic to split hair, let's just not target ads at one gender.
Knowing what a type of person wants on the average is not discrimination.
Your example of listing a job in Men's Health but not Cosmopolitan seems good. Technically not a perfect analogue as a woman always could buy Men's Health, but in practice very similar.
Spinning off into a different angle, what if an advertiser gets the most qualified female applicants advertising through LinkedIn, and the most qualified male applicants through Facebook? (Again assuming pay per view) Is it wrong for them to target women & men on separate platforms with separate ads? Utterly hypothetical of course.
Or yet a different angle, what if they have ad "A" and ad "B", each subtly designed to excite one of the sexes. Perhaps an ad for the Marines, one emphasizing toughness & grit, the other emphasizing teamwork & "stronger together". Target one at men, one at women. Legal?
To me it seems to come down to the overall behavior of the employer, not Facebook or any one ad.