Why does God allow natural disasters?
God allows natural disasters because they are natural. This may sound like too simple an answer, but I believe it is the correct answer. God created a universe in which planets sustain life. In order for a planet to sustain life, it must have what we call plate tectonics, because the recycling that goes on in plate tectonics does two things. First, it recycles the minerals in the earth so that advanced life forms can exist. Second, it produces, or more accurately, sustains an atmosphere. God created a universe in which plate tectonics are “natural.” If he had not, then we would not be here. It just so happens that plate tectonics also causes volcanoes and earthquakes. These are called natural disasters for a good reason. God created a world which functions beautifully and amazingly to support life, but that world has volcanoes and earthquakes. If the critic of God can conceive of a better universe, then I ask them to do so. After conceiving of a better universe, then they will need to actually create that universe.
A second example. God created a universe in which galaxies, stars and planets form naturally. Gravity, which God created, does the work of creating these objects. Good plan, God! Gravity creates spherical objects naturally. Because the earth is spherical, the energy from the sun which sustains life on the earth (also an amazing invention of our Creator) is not distributed evenly. So, God invented what we call weather to move that energy around. Weather is required for life, obviously, but weather also produces natural disasters. These are, by definition, natural. If God wanted to prevent weather, I suppose he could, but then how would the energy from the sun be distributed to sustain life over most of the sphere of the earth. Again, if someone can propose a better set of natural laws, then I ask that person to propose a better universe than the one we live in, but I say to God, “good job!”
The question you are asking is coming with an unstated assumption behind it, which is that a loving and powerful God would prevent natural disasters. I disagree. Death is not the human problem. Sin is the human problem. God is in the business of preventing sin, not preventing natural disasters, but he gives us free will. Natural disasters are tragic for us humans, and God has compassion on us for that reason, but natural disasters are not disasters to God.
Natural disasters, including diseases and death in general, are not bad things. They are not things which God ought to prevent. This is why God allows natural disasters. They are a natural part of an incredibly designed universe–designed by the Creator so that life can be naturally sustained.