They heard it on a meme, and I'm not saying that as a joke. Specifically, there was an instance (9 months before Obama was elected, he was not even the nominee yet) when Michelle Obama was saying how she is proud of America for the first time in her adult life because people all over the country seem genuinely hungry for change. It was a pretty typical campaign speech.
They started making memes of her where they twisted her words into something entirely different. They used that quote to claim that she hated America until Barack (a black man) was elected. Then used that as evidence to claim she's racist against white people.
Of course, Barack was not elected yet, he was not even the nominee yet. She also was not talking about race at all, not remotely close. She was talking about seeing people from red and blue states unified behind a common message of hope. There was nothing race related there at all.
People on this forum are still lying about this though. Just recently I had to explain to another poster how he was duped by the meme like a decade ago, and he never let it go. He said that was all it took, and he hated her forever because of it. That black Sheriff that conservatives love, David Clark, he goes around saying it too (he's a lying political hack, but they like that kinda thing).
