This principle that only strongest survive is incorrect. Everyone has their role and even if one species tries hard to destroy another species, they will find a way to survive. Mosquitoes are probably the biggest killer of humans other than natural causes in this world. But still they survive in spite of all the efforts by us to eradicate them.
Moreover, animals usually do not kill for fun like humans do. They are not as jealous as humans. They are not as greedy as humans. We are the deadliest species on this planet who not only want to destroy other species but others of the our species as well.