Why do terrible natural disasters—earthquakes, tsunamis, droughts, volcanic eruptions, and disease—occur, and do they come from the hand of God? What kind of God would let such things happen, or be directly involved in them? What kind of control does God have over creation?
The key answer here can be summed up in one word: SIN. Without it, we have a world free of suffering, free of pain, and free of natural disasters. With it, we must deal with its consequences. The reason we question God when disasters strike? Mainly, because we are appealing to a universal law that guides the world, and we want to know why it is broken-and innately assuming that God has let it become broken when it is in fact us that has strayed.
CS Lewis once said, "You cannot tell a crooked line from a straight one." When we cry out for answers, we assume something is wrong, terribly wrong. That feeling is a natural appeal to a universal law that governs the universe.
Another way to tackle the question is the following badger back and forth:
Q: Why is there so much evil in the world?
A: If there is such a thing as evil, there must be such a thing as good.
A2: If there is such a thing as good, there must be something above, namely a moral law, to differentiate between that which is good and evil (The crooked line from the straight line).
A3: If there is a moral law, must there not be a moral law giver? Yet that is what one is trying to disprove and not prove by asking the initial question.
Natural Disasters that destroy people, their lives, and homes were not initially in God's plan for mankind. SIN initiated the flood that wiped out mankind and SIN is what leads to the natural disasters we see today. Whether or not that disaster is an act of judgment of a holy God or a result of nature gone bad is another issue. Regardless, our initial reaction of questioning God is really an acknowledgment that God exists and his will for creation has been violated.
The following Seminary Article may provide some additional answers on the topic.