First: I am definitely not in the "women are superior" camp.
however, there are a lot of bad examples here. If I wanted an expert opinion I would ask an expert. If I wanted to learn a new language I would be asking a woman because I know far more bilingual women as opposed to men. In my experience women are leaps and bounds better than men when it comes to language. If I wanted to learn a sport I would ask my dad. If I wanted to buy a nice camera and learn to use it I would ask a woman because I know more female photographers than men who have heavily researched before making a purchase. It makes no sense to present the hypothetical of needing expert advice and asking us to select a gender. I would ask the expert.
I think it's funny that you included any kind of emotional support. I am incredibly unlikely to go to a man to work out my feels. If I need courage or really anything involving emotion I will go to a woman 90% of the time. And as a woman I would definitely not ask a man how to get in shape. Women's bodies work differently. A man can only give me theory. A woman can give me theory along with first hand knowledge.
As for the rest, most of the time (which is to say, almost every single time and with few exceptions) I would choose a man. If you wanted to stack this list heavily in favor of men you could have done a much better job. On the grand scale (meaning counting average people) I'm not sure I agree (not sure I agree =/= disagree, mind you) that men are superior, but I do think that the top tier of men are superior to the top tier of women.
Do you really think that a man is a better choice for all of these? That's just really weird to me based on some of these examples. I respect my Husband more than anyone on the planet, but I literally LOL'd at the thought of coming to him to help me work out my emotions or really anything to do with learning how to communicate more effectively. Almost never would I go to a man for anything relating to that subject, and I can't imagine why on earth anyone would think a man is better suited for that task. Thanks for the giggles though.