From a theological perspective I consider this to be a tougher question than “why do humans suffer“.
I believe that we have to return to the premise that God purposes to create a world within which humans become his reflection in exercising free will in a perfect way. What we currently observe is a “work in progress” towards that objective. Once we come to grips with the realization that such a world seems almost paradoxically impossible then we also realize that there are probably some parameters which are incomprehensible to us at present. Since God by definition would always take the best option in to achieve his purpose, we can only work on the basis that what we see around us is indeed the best option, even if some elements of it seem out of place to us.
The reality is that suffering is subjective in the first place, and we simply have no idea what level of suffering animals experience – both physically and psychologically. However I personally would not hide behind some sort of pretence that animals don’t really suffer at all. I am a firm believer from personal observation that animals reflect emotions of fear and experience pain similar to our own.
Of course a great deal of animal suffering can be attributed to humans who abuse the natural environment. Man was originally assigned the task of care taking the earth (Gen 1:28). Had they done so perfectly then we can imagine quite a different scenario to what we see now. That said, it would certainly appear that animal suffering precedes the appearance of humanity on the scene. We can infer from evidence of predation and disease in the fossil records that animals probably suffered to some degree even during the creation process.
One important factor to consider is that, if humanity is to reflect God’s quality of love at all times, even with perfect free will, then it is plausible that man could not conceive of love without observing an environment which simultaneously demonstrates God’s love AND pure free will as exercised by creatures acting on instinct alone.
The food chain is clearly a practical creation, but along with disease and decay, may also be intended to serve a demonstrative purpose.
One thing is for sure – we do not know exactly how things will be ordered in the “new heavens and new earth” that we await according to God’s promise (2 Peter 3:13). Will animal suffering continue in that environment. There are certain prophetic scriptures that indicate peace in the animal realm as well as the human one.
The wolf shall dwell with the lamb, and the leopard shall lie down with the young goat, and the calf and the lion and the fattened calf together; and a little child shall lead them.
The wolf and the lamb shall graze together; the lion shall eat straw like the ox, and dust shall be the serpent’s food. They shall not hurt or destroy in all my holy mountain,” says the LORD.
Whether these promise are literal or not, temporary or not, only time will tell.