There's an in-game book, found in all three games, that describes where Witchers come from. It was a propaganda book, and it's full of lies. I think the people you were talking to must have got their information from that.
But it's not true. Like all witchers, Geralt was born human, and his parents were human. He was mutated during a process called the Trial of Grasses when he was a boy.
"who would allow their kids to become a witcher" - these were difficult times. There were a lot of orphans, children whose parents couldn't afford to keep them, children who may have otherwise died. Some were given in payment of debt, because a Witcher had save the parents. Of those taken into the Witcher schools, most still didn't survive, the training or the Trial killed them. But some did.