Several species will do this such as many types of insects and spiders, some monkies (chimpanzess), and sometimes male lions. There are different reasons for this behavior in each species.
Many animals will kill their own offspring. Certain birds will push a baby out of the nest if appears weak. Gorillas have also been known to eat their young.
A lot of animals kill their offspring. Hamsters will eat them, and cats will abandon unhealthy kittens. Even post-partum pyschotic humans will kill their kids.