The pokemon in the anime cannot learn more than 4 moves. If you watched the whole series starting from gen 1, you will find that when a pokemon learns a new move, it doesn't use one of its moves anymore. Pikachu is a example; before pikachu learned electro ball or some other move I can't remember, it knew volt tackle. That was in gen 5(I think). After it learned a new move, it stopped using volt tackle. Meaning that it has forgotten volt tackle.