The latest in the Stuff People Get Wrong series.
Prepositions mess people up a lot. You do things "on purpose" and you do things "by accident". "On accident" comes up by combining the two. This one can be avoided altogether by using the synonym "accidentally".
While digging up the root cause of this I was unsuccessful in what makes "on accident" common among children. Several theories include the parallelism to "on purpose" or the idea that children go with "what sounds right" when forming preposition use.