Ok, here goes my highly controversial sweeping generalization: men suck at multitasking, women are actually much better at it. My source? Just years of active observation. I'd be very interested to see any actual research on the subject.
So it's not so black and white, men shouldn't multi-task but women can. More like, multi-tasking is bad for both genders but not as bad for women as for men.
I'd call you sexist, but my sample size of one smashed femur by a female left turner who didn't see me fails to disprove your theory.
The impression that we can do more when multitasking is our own illusion.
Ironically playing action games improves your task switching ability, but you still do worse than if you unitasked.