Why do ladybugs eat their own eggs?

well because it does not have a lot of plants or it want to get more energy. Ladybugs get more energy eating other insects.

You would have to go back many thousands of years to find that answer. That is simply what they do, based on what they are. For the same reason that lions are carnivores and cows are not. There are a couple of species of lady beetles that do eat plants only and sometimes feed on crops (e.g., the squash beetle and the Mexican bean beetle).