I'm pretty sure that random female co-workers can't actually coerce you into doing anything that you don't want to do. More likely, they're just better at persuading you to do something, and this could be attributed to women having better-developed social skills (without having to hypothesize some kind of "female approval" dynamic).
Why is inventing something that makes no sense "women have better social skills" a good plan, but a well known observation "women's social interactions confer social status on men" bad? What social skills are women using to get the men in the office to carry boxes of paper? Do you seriously think a man could just practice socializing really hard and suddenly be able to ask another man to do that and have it work?