It's possible that you ended up hacking your game, that is really the only cause for Bad Eggs in recent Pokémon games. If a hack is possibly a bad or incorrect hack then you could get a Bad Egg.
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By using a AR and catching someones Pokemon it will be called bad egg
If you are talking about the bad egg, it does not. That's why it is called a bad egg.
you get it from an egg in Pokemon platinum
There is absolutely no way to hatch it.
You can not get a Turtwig egg in Pokemon Platinum. But if you breed a Turtwig with a Ditto, then it is possible.