ANSWER: Today there exists two major classes of animals that eat meat. The first, called omnivores (e.g. bears), live off a mix of both flesh and plant based food sources. The second class of animals, called carnivores (e.g. lions, tigers, snakes, etc.), solely or primarily consume flesh as the main part of their diet.
Scripture clearly states that God did not require animals (and even humans) to ingest meat as part of their diets. All living things were commanded to eat only plant-based foods for their daily sustenance (Genesis 1:29 - 30).
God did not create animals to be predators and eat each other. He did not create beasts that needed to hunt down, kill, tear up and devour their fellow creatures. He brought everything into existence in a state of perfection. This perfection is based on his way of life, which is founded on selfless love for others (1John 4:8). In the Garden of Eden he states that everything brought into existence was "exceedingly good," including the animals (Genesis 1:31).
This perfection manifested itself when, before sin entered the world, Adam was blessed with the task of naming all land-based creatures including birds (Genesis 2:19). There is no indication that any lion, bear, or other present day carnivores tried to attack or kill him during this process. All life was gentle and docile.
What, then, caused a monumental change in the nature of many animals such that they added eating meat to their diet? How did creatures, originally peaceful, become predatory? Two major factors led to this radical departure from what was originally intended.
When Adam and Eve sinned by taking from the tree of good and evil, they rejected trusting in God and replaced it with believing in Satan's (and their own) deceptions. This sin brought with it manifold consequences that affected not only the physical world (e.g. animals) but also the spiritual one.
The first humans, from the moment they disobeyed, began to decline, ultimately leading to their death (Genesis 2:17, 3:3). Their sin also condemned all humans to die as well (Romans 5:12, 1Corinthians 15:21 - 22). Additionally, it introduced curses into all animals (Genesis 3:14) and even the plant world (3:17 - 19, 5:29).
The second factor that also led to some animals (and even some plants) eating meat is Satan himself. The rebellion of our first parents allowed the devil, as a god or prince, to rule over the earth and pervert all things within it (John 12:31, 14:30, 16:11, Ephesians 2:2, 6:12, etc.). The influence of our adversary's competitive way of life, coupled with his complete willingness to kill at any time (see John 8:44, Revelation 12:1 - 4), has permeated the instinct of many living things like animals.
A Restoration of Peace
Biblical prophecies indicate that the present predatory nature of animals, and their desire to eat meat, will be removed during the millennial reign of Christ. The prophet Isaiah specifically mentions that the wolf, leopard, lion and bear will soon return to being herbivores (consuming solely plant-based food). Even humans and vipers (the KJV calls them cockatrices) will coexist in harmony (Isaiah 11:6 - 8)!