Why Does Allah Allow Suffering?
Question

How do we explain God to someone who believes that while God exists, they cannot accept or understand how a merciful, compassionate God would allow so much human suffering to take place? The analogy they give is that if we are God's children, why does God not protect us -- just as a parent would guard over their children?
Praise be to Allah.Allah (God) Almighty, is most merciful and compassionate, without any doubt. Yet His actions cannot be fully comprehended by our incompetent minds. 
What simplifies this issue is that we all agree that Allah is fair, just, wise and knowing. That means whatever He-Almighty- does, is with a legitimate purpose although we may not be able to understand, just why.  
For example, a caring and loving doctor and father may be forced to amputate the leg of his only son. There is no doubt that this father loves his son. Yet his action was for the sake of this beloved son, although it may seem cruel to those who do not understand the circumstances. 
Allah Almighty has the greater and higher example, and it is not to any of His creatures to question His doings as it is mentioned in the Quran (interpretations of the meaning): 
“He cannot be questioned about what He does, but they will all be questioned.” [Al-Anbiya’ 21:23]
It is a Muslim’s belief that suffering of pain, hunger, tragic accidents etc., are due to one's sins, and Allah decrees this suffering to act as a means of erasing these sins which were committed by this Muslim. Allah says in the Quran (interpretations of the meaning):
“Whatever affliction befalls you is because of what your own hands have committed. And He pardons much.” [Ash-Shu`ara 42:30]
It is also apparent that man in times of crisis gets closer to Allah and starts repenting, while in times of ease and comfort he is far from remembering the blessings of Allah and he uses these gifts and blessings in committing sin after sin.
Allah the Almighty has shown man the path of good and evil, and he gave him the power and will to choose. Therefore, man is accountable to his deeds and the punishment he receives for them, for life in this world is merely a test, but the results are to be known in the Hereafter.
For more details, please refer to the following answers: 20785 , 13610 , 71236 , 35914 , 22798 , 124504 , 112905 , 21631 .
And Allah knows best.