Why can't women hold Mormon priesthood, or be prophet, or bishop, or Mission president, or give blessings?

It goes back to the tradition of the man of the house standing as patriarch of the home. Women don't need the priesthood but still able enjoy all the blessings of it. They are however able to give 'faith' blessings but not able to administer in the priesthood with regards to preparing, passing, blessing the sacrament for example. The other fact is that women simply do not need the priesthood due to their own, equally important role as a mother, to nurture and care for her children.