Think of it this way: How many things can you come up with that a woman can do that a man can't. If a man needs something like that done, he has to convey his wishes to a woman. Thing is, men CAN clean the house, men CAN change a diaper etc etc. So one by one, other than "have my baby", there are very few things that men can reasonably say "I can't do that, you have to do it for me."
So - if a guy tries to tell a woman to do something, he is a failure because he should be able to do it himself. The mindset changes: If he tells her to do something, he is a cross between being a prick and/or being dependent.
But there remain a large number of things that we expect women to ask men to do, all variations of "open this jar for me". Women are used to being considered dependent. When we say that a woman needs a man like a fish needs a bicycle, we're assuming that there is always somebody bigger/stronger/whatever to get things done, and what we're really saying is that a woman needs a SPECIFIC man like a fish needs a bicycle.
Our society is used to having women ask for help. It discourages men from asking for help.
After awhile, "could you open this jar" becomes "open this jar". And yes, there is a sense of entitlement that comes with that, equating to getting angry when the jar doesn't get open.