You are 100% correct, but when you say there are some chores which men cannot do I disagree with that because I once had a neighbour who give birth to only 2 boys. She raised those male children like girls. There is no kind of chores those children can not do. They can also make varieties of dishes even more delicious than the one any woman will prepare.
In that regard I must say that we women are indeed helping hands and we do all that because culture demands that from us but if you train a male child in that manner he will grow up with that character also