Okay, that marriage thing ... this is the first time I heard it.
What's the offspring between a human and Pokémon?
A human kid or Pokémon kid?
It's never stated. On one hand, I presume human genetics is just too different from pokémon genetics to be recognised. On the other hand almost all pokémon are egg-laying pokémon, the rest simply non-binary or unable to reproduce.
A fan theory of mine is that in the world of pokémon there are no regular animals. Pokémon are the animals though some more advance than others. (I've heard various fan theories that pokémon originated from the moon or that Mew is the progenitor pokémon.)
If it's true, that would explain why humans and pokémon share a world as sole lifeforms. (though "
pokérus" is often described as a microscopic lifeform than boost a pokémons health than harm it, so it could be possible the world of Pokémon is shared with other non-pokémon lifeforms.)
As I mentioned before, pokémon and humans have likely an evolved mutualism. It's why humans can't shoot lasers from their mouths like pokémon nor you can't find a Level 100 pikachu in the wilds because pokémon can only grow as strong by themselves. But once partnered with a human, they can exceed their strengths and abilities.
I don't know much on in-lore Pokémon history on how long humans and pokémon have been training together, Pokemon history shows pokémon and humans co-existing for at least 10,000 years. But it could be possible pokemon recognise humans for their higher intelligence, which is why pokémon seem rather chill and quick to co-operate with humans after capture as if it's natural for them.