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Mew was the original Pokemon. According to canon sources, Mew slowly evolved (Darwinian evolution, not Pokemon evolution) into all the Pokemon we know today. With its embryo-like appearance, this makes sense.
All the other pixie legendaries are the stepping stones between Mew and modern Pokemon. Each one represents an egg group, but keeps similar stats and appearance to Mew in order to show their similarity.
Mew: Ditto (the original; containing the DNA of/able to take the form of all Pokemon)
Celebi: Grass
Jirachi: Amorphous/Fairy/Mineral
Manaphy: Water 3
Victini: Field/Monster
Diancie: Mineral (if it counts as a pixie)