Let us first present some examples, and your human intellect will automatically guide you that these inheritance laws are unjust and devoid of any wisdom.

There are many online Islamic Inheritance Calculators present online. For example:

Please use any online calculator to verify the following examples. 

1st Example: Old Widow will get 25%, while a "MALE" relative (even a distant one like cousin, or his son, or his grandson) will get 75% 

If the deceased person has no children, but only a wife, and only a distant male relative, then they will get shares as under:

Relative Share Fraction Share Percentage
Wife
1/4
25%

Any distant male Relative like 
Cousin (or even his descendents)

3/4
75%

A wife stays with her husband the whole of her life. But when she is old and becomes a widow, then she will get only 25% of inheritance. While the 75% inheritance goes to any distant male relative, like cousin (or any of his descendent), whom the deceased person might not have seen in his entire life. 

  • Does this make any sense to you?
  • Do you see any Divine Wisdom in this Islamic law?
  • Do you think Muhammad/Allah has done justice with women here?

But the opposite is not valid, i.e. if a woman dies then the Husband will inherit all her property, despite the presence of her distant relatives. 

2nd Example: Mother will get 33.33%, while distant relatives (like cousins, or his son, or his grandson) will get 66.67%

Similarly, if a deceased person has only an old mother and a distant male relative, then they will get their share as under.

Relative Share Fraction Share Percentage
Mother
1/3
33.33%

Any distant male Relative like 
Cousin (or even his descendents)

2/3
66.67%

So, the old mother will get only 33.33%, while a cousin (or his descendents, whom the deceased person might not have seen in his entire life) will get 66.67%.

Why?

Do you see any divine WISDOM here?

3rd Example: Sister will get much more share in inheritance than the mother and the wife

Even if the sister is married, still she will get more share in inheritance than mother. 

Relative Share Fraction Share Percentage
Mother 2/5 40%
Sister 3/5 60%

Mother is more closely related to her son, then brother/sister relationship. But the illogical division of shares by Quran made it happen that a sister gets more than mother in inheritance (even if the sister is married). 

Moreover, a widow will get even less than the mother, and the sister's share will become even bigger. 

Relative Share Fraction Share Percentage
Wife 1/4 25%
Sister 3/4 75%

Moreover, even if a deceased person has a daughter, still half of the property will go to the sister (even if she is married). 

Relative Share Fraction Share Percentage
Daughter 1/2 50%
Sister 1/2 50%

All these unjust and ridiculous shares are a product of illogical Islamic laws of inheritance, which are devoid of any divine wisdom. 

 

Islamic LOGIC : A woman will get only HALF as compared to the man

(Taken from a post of Ex-Muslim_HOTD)

Ibn al-Qayyim explains the Islamic logic, why women receive half:

As for inheritance, the wisdom of preference (for the male) is obvious. The male is in greater need of the money than the female because men are supporting women. And the male is more beneficial than a female to the deceased while he is alive.

Ibn al-Qayyim, Ilam al-Muwaqqin an Rabb al-Alamin 2/115

Several points:

1- Inheritance is a one-time benefit, independent of who is working to financially support the family. A woman can use inheritance for the benefit of her spouse and family just as capably as a man can.

2- The rules are excessively rigid and do not adapt to the unique circumstances of each family.

3- It is bizarrely unfair. Imagine a wealthy parent who dies, leaving only a married son and a married daughter, both wanting to start their own families. It is illogical that the son gets double the wealth of the daughter. The most equitable scenario would be that the son and daughter receive the same amount and both new families equally benefit.

4- Half-a-man does not make sense for spousal inheritance because the widow typically has no source of income. As a very simple example, imagine a married couple, 50 years old, with no kids. The wife receives only 25% from her deceased husband, but the husband receives 50% from his deceased wife.

If anything, the wife should receive a HIGHER share, especially in an Islamic society, because: 1) her employment prospects are poor, and 2) her prospects of getting remarried—and thus financially supported—in her 50's are poor. She likely will have to fend the rest of her life with no income.

5- Given Islam's logic, the premise must be that the woman does not earn income. If a woman earns income, as plenty of Muslim women do, then she should receive more than half of a man. In fact, if a woman earns similar income to her husband and still does the bulk of the housework, she deserves more than the man.

6- The last point made by Ibn al-Qayyim--"And the male is more beneficial than a female to the deceased while he is alive"--is particularly dubious. I do not feel that my son has been “more beneficial” to me than my daughter, and that certainly should not be justification for me giving my son double the inheritance of my daughter.

Bottom line, "Allah's” one-size-fits-all inheritance rules poorly adapt to the unique circumstances of every family—and are sexist to boot.