The Qur'an has given equal share to women with the exception...
The Qur'an has given equal share to women with the exception of the daughter of the deceased. For just this instance we are informed by the Qur'an that the share of a son is equal to that of two daughters: "Allah enjoins you concerning your children: The male shall have the equal of the portion of two females.." (4:11) To comprehend the reason for this division, it should be understood that the Qur'an establishes a society in which responsibility of acquiring livelihood lies with the men and it is not an obligation on women to provide for her husband and family.
A woman is also incapacitated during certain periods due to her natural disposition (pregnancy). It is thus apparent that a man should get a larger portion from the division of resources, as he has been laid with the responsibility of the provision of maintenance to his family. That is why, in inheritance, boy's share has been kept twice as much of a girl. Daughters have neither been made responsible for their own, nor their family's expenditure.
But on the other hand, a son has to maintain not only himself, but his wife and family as well. As such, he should be vested with a larger share. Where the dispersion of inheritance is amidst the people of the same generation, as is the case of a brother and sister (in case the deceased was issue-less and parents were still living) each of them gets one sixth (equal).
"..and if a man or a woman leaves property to be inherited by neither parents nor offspring, and he (or she) has a brother or a sister, then each of them two shall have the sixth.." (4:12) For parents, it is again one sixth each for mother and father.
"..and as for his parents, each of them shall have the sixth of what he has left if he has a child.." (4:11) Therefore, it is not correct to state that the Quran has made a general rule that the woman's share is half of the man's; it is only so for sons and daughters, members of the future generation or others where the situation is similar that the male is alloted more than the female.
On the other hand, in a situation in which men are neglecting this duty of theirs and it is feared that the woman would be rendered impoverished, the Quran gives authority that, in a will, a person can divide his property as he pleases according to the dire straits of the circumstances. The division of inheritance as given in the Quran is only applicable if a person dies without leaving a will, or if his will does not cover all his whole property.