My friend and I were wondering why Mew has an Egg Cycle if it can't be bred, because that would mean Mew would have had to been bred to be in an egg to hatch...or am I wrong?
It is because in the game My Pokemon Ranch for Wii Wares, you are given a mew egg. When you import 999 Pokemon to the game, Haley, the NPC that's helping you, will give you an egg containing mew. Haley will give you an egg prior to giving the mew egg, this egg contains phione. This phione egg is obtained by reaching 250 transphered Pokemon
(Source)
Hope I helped