There are multiple reasons why cats, specifically big cats like lions, will decide to eat their young. Male lions will sometimes eat the young in a pride that he has recently taken over in order to encourage mating with the females of that pride. Female-instigated infanticide is less common than male, but it still occurs.
One reason a female cat might kill her young is to control the litter size based on her own abilities to raise them. Another reason is that she simply desires to mate with a particular male cat.
Female- and male-instigated infanticide is also common in captivity, such as what is seen with lions in zoos. Many experts believe that the added stress of captivity causes many of these occurrences of infanticide. Some who disagree claim that zoos remove the stress of possible starvation and other harsh factors of the wild, and therefore infanticide should decrease. However, others say that captivity adds additional stress, such as the confined spaces in which these animals, who are naturally accustomed to wide, open spaces, must live.
Others agree that infanticide must be taken at an individual case, based on the individual cat. This is to say that some cats will kill or abandon their young, while others in the same or similar conditions will not and actually become good, nurturing mothers.