It's a misleading and dangerous line of reasoning to pursue, however. Since we read in James 1:13 that God is not tempted by evil, nor does He tempt us, it would be impossible for Him to be the source of such suffering. This is simply an example of what the CCC calls "physical evil" as opposed to "moral evil". The world is a complicated machine in which God does not constantly insert His hand when something is about to break and cause harm. He permits nature to run its course. To do otherwise, would be heaven, and we're not there yet (except in Mass, as Scott Hahn might say).
Here's a small part of what the Catholic Encyclopedia offers on the three different dimensions of evil. (I'm not sure I've ever actually heard of "metaphysical evil" before. It's also not mentioned once in the entire Catechism of the Catholic Church.)
With regard to the nature of evil, it should be observed that evil is of three kinds — physical, moral, and metaphysical. Physical evil includes all that causes harm to man, whether by bodily injury, by thwarting his natural desires, or by preventing the full development of his powers, either in the order of nature directly, or through the various social conditions under which mankind naturally exists. Physical evils directly due to nature are sickness, accident, death, etc. Poverty, oppression, and some forms of disease are instances of evil arising from imperfect social organization. Mental suffering, such as anxiety, disappointment, and remorse, and the limitation of intelligence which prevents humans beings from attaining to the full comprehension of their environment, are congenital forms of evil each vary in character and degree according to natural disposition and social circumstances.
Are all types of pain and suffering, then, because of the Fall of Man? The simple answer is Yes. The choice of Adam and Eve, already created in the image of God, to disobey their Creator in a tragically misguided attempt to be "like God," led to evil being allowed to enter the world, permanently changing every facet and dimension of our lives. With the barrier of sin now present between us and our Heavenly Father, however, God never gave up on mankind, but He continually sought to give us the means to seek and receive redemption and freedom from the sin. While the sin weakens us, the suffering may build spiritual strength and endurance.
The simple answer to Why does God allow suffering? is really impossible until we first have a solid understanding of the nature of sin and evil. Once that is understood, we can say that suffering allows us to become the people God created us to be, refined by fire as it were. As previously mentioned, God allows our broken world to run its course. When my grandmother lay dying in a coma some years ago in a small hospital room overlooking the brilliant fall tapestry of the Yakima Valley below, I remarked to my grandfather "that it wasn't ever supposed to be this way." By that statement, I was trying to say that God had other plans for us--even though his omniscient nature was fully aware that we would fail. If there was no free will, we could not truly say that we could independently love God; we would be automatons, machines. Likewise, suffering may also be tied to this free will. We are held accountable for our bad choices and decisions--sin being the worst.
Along our journey, it’s important to remember that every person we meet within our hectic daily schedules is someone for whom Christ’s blood was spilled, and, therefore, a fellow member or potential member, of the Body of Christ. As C.S. Lewis reminds us in The Weight of Glory, there aren’t “ordinary people.” We all have everlasting souls. We are familiar perhaps with the idea of redemptive suffering, offering our pains and struggles up to God. If we can apply this kind of internal reverence to our daily lives, we are offering these routine activities up to Christ. In this way, we are also acknowledging that we our identity is greater than what our daily life may trick us to believe. That is, our identity should not necessarily be tied so closely to our work or vocation. We are more than what we do from 8-5; our jobs should not define us. When we understand this, we are transforming the mundane to the eternal as we strive to live Paul’s words from 1 Corinthians 10:31: “whatever you do, do for the glory of God.”
Not only may suffering lead us to a closer union with Christ, but God can bring good out of the evils we face. In conclusion, here is a passage from Saint Thomas Aquinas' masterpiece Summa Theologica. It's also followed by a short quote from C.S. Lewis' The Problem of Pain. Following this, I have also listed some additional reading suggestions, but I have intentionally kept the list very brief.
I answer that, It must be said that every evil in some way has a cause. For evil is the absence of the good, which is natural and due to a thing. But that anything fail from its natural and due disposition can come only from some cause drawing it out of its proper disposition. For a heavy thing is not moved upwards except by some impelling force; nor does an agent fail in its action except from some impediment... (Saint Thomas)
Pain hurts. That is what the word means. I am only trying to show that the old Christian doctrine of being made perfect through suffering is not incredible. To prove it palatable is beyond my design. (C.S. Lewis)
Summa Theologica, Saint Thomas Aquinas
The Problem of Pain, C.S. Lewis
Grief Observed, C.S. Lewis
The Catechism of the Catholic Church
Providence and the scandal of evil (Why does evil exist?) Read CCC# 309
God’s Wisdom: He created it in a “state of journeying”, “With physical good there exists also physical evil as long as creation has not reached perfection.” CCC # 310
Free Will: “Angels and men, as intelligent and free creatures, have to journey toward their ultimate destinies by their free choice and preferential love.” CCC #311
God is all powerful: He causes Good out of evil. CCC #312
“We know that in everything God works for good for those who love him.” Rom. 8:28
His ways are unknown to us. “Only at the end when our partial knowledge ceases…” will we understand. CCC #314