The problem of evil is perplexing to believers and unbelievers alike. If God is all knowing, all powerful, and all good, why is the world so wretched? There are multiple layers to this problem. There's the existence of demons, there's the sin of man, there's the state of the animal kingdom, there's disease, there are natural disasters. All of these things have a general answer: Sin, and the glory of God. But there are more specific answers, and ultimately entire books could be dedicated just to what we know.
In Leviticus 26:6, dangerous animals are specifically mentioned. Dangerous animals are, of course, a threat to mankind. Even today animals cause serious problems, but historically, aside from there being more dangerous animals roaming the lands which are now extinct, mankind had less effective defences against them. Would you rather fight a hippo with a gun, or a dinosaur with a wooden staff?
In the Garden of Eden, this was not the case. Mankind had dominion over the completely vegetarian (Genesis 1:30) animal kingdom. Man was completely at peace with God, and so everything was at peace with man. When man sinned, everything changed. The very ground was cursed, and along with it, our relationship with the animals was severely damaged.
One of the ways God shows His favor is the reduction of the curse. God revealed His favor to Israel by removing dangerous animals from their lands. By contrast, God's wrath often includes the use of animals. Cursed cities, for example, are often completely given over to animals (e.g. Isaiah 34:13).
Thus, one of many reasons dangerous animals exist, and are so dangerous, is to allow God to both execute judgments against sinners and to give Him one way to show His favor.