Why does God permit suffering?

It was not God who introduced suffering into the universe. It was Lucifer, who became Satan; the devil. It is for the sake of those who will inhabit the universe for all eternity that God allows Satan to demonstrate sufficiently what the true course of sin really is. But you ask, "Isn't it enough? Haven't we seen enough?" Let me ask you: "Has mankind learned their lesson? Is war obsolete? Has crime ceased?" One of the sad facts of life is that some will never learn the lesson! Following in the footsteps of Satan himself, they will carry their rebellion against God to the bitter end. Only God knows when it will be safe to eliminate sin and those who perpetrate it from the universe without allowing cause for it to ever return again. Remember, sin can only enter the universe through the mind of a rational being. It is the result of the misuse of the freedom of choice. God's creatures will retain their free will, but none will ever choose rebellion against God again. The prophet Nahum says, "affiliation shall not rise up the second time."
God will gain and hold the voluntary allegiance of His loyal children for all eternity. He will not do this through fear. He will do it through love. It will yet be proven that every act of God, even the destruction of the wicked, will be an act of love. One indication of God's love is the suffering that He Himself has endured through the entire great controversy begun by Lucifer's rebellion. Even with modern inventions like television, we see only a tiny portion of the suffering in the world. God sees it all, every second, every hour, night and day, without holidays or vacations! It is Satan who enjoys watching people suffer, and not because of his hatred for us. Satan knows how much it hurts God to watch His children suffer, and God is the object of his hatred. To Satan, we are merely pawns in his game. To God, we are the objects of His supreme affections. Even the destruction of Satan can bring no joy to the heart of God. He remembers him as he once was, and as he could have been.
The day is coming when peace, genuine peace, will reign throughout the entire universe. The Bible is the guide to how this peace will be established and how it will be maintained. When God's plan of restoration is completed, the effects of Lucifer's rebellion will be forever gone. The universe will be no better for it. God would have preferred that it never have had to happen. But the universe will be safe from the danger of it ever happening again.

"And I heard a great voice out of heaven saying, Behold, the tabernacle of God is with men, and he will dwell with them, and they shall be his people, and God himself shall be with them, and be their God.
And God shall wipe away all tears from their eyes: and there shall be no more death, neither sorrow, nor crying, neither shall there be any more pain: for the former things are passed away." Revelation 21:3-4