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Pokémon and humans used to live together as the do in the main series games. At some point in the future for whatever reason, humans are at war with each other again and Pokémon are weaponized against each other. (Imagine the war from the intro to the Lucario movie, only now with tanks and shit.) By the end of the war, there are millions of human and Pokémon casualties.
Arceus, enraged with seeing Pokémon employed against each other in fights to the death, punishes the humans by separating the human and Pokémon worlds forever, and erasing all memories that the humans and Pokémon had of living together.
The Pokémon now live in the world depicted in the Mystery Dungeon games, where humans are thought just to be mythical creatures of legend. Once in a while, a human is plucked from his or her world, imprisoned in a Pokémon body, and employed to help preserve the balance of the Pokémon world. The reverse doesn't occur because Arceus has forsaken the humans, and does not care what becomes of their world.
The humans in their world go on with their lives much like we do. All of the images and motifs of the Pokémon that once lived with the humans are simply thought of as a global fad of some older time. Here, Pokémon live on as mere children's toys and games.