Why does the female inherit half of what the male inherits, while the parents inherit equally upon a man's death?

A woman's inheritance varies in different situations: she may inherit half the share of a man, as in the case of a daughter with her male brother, or a mother with a father if there are no children. She may also inherit the same as him, such as a mother and father when a son is present, or a brother and sister from the mother's side. She may even inherit more than him, as in the case of a husband with his two daughters, or a husband with his only daughter. A woman may also inherit while her male counterpart does not, as in the case of a son's daughter who inherits one-sixth if there is no remaining share for a son's son if he were in her place. Allah has wisdom in preferring men in some cases, as men are obligated to provide for their families and pay the dowry and similar expenses, while women are not burdened with such obligations.