The answer is there are few effective predators of rabbits.
When a new species is introduced into some area, it could very soon increase its population size if there are no natural predators. Predators maintain prey population on some optimal size and that way homeostasis in ecosystem is achieved. Without natural predators, rabbit population will increase its size. With more rabbits in the area, many native species will decrease their population size because they must compete with rabbit population for resources.