A contrary person; someone who is stubborn, moody, or takes a contrary attitude (a sourpuss).
あの先生はひねくれ者で、褒めても素直に受け取らない。
That teacher is a curmudgeon; even if you praise them they won't accept it graciously.
子どものころ、みんなからひねくれ者だと言われた。
When I was a child, everyone called me a contrary kid.
彼は少しひねくれ者のところがあるが、実は優しい。
He's a bit of a sourpuss, but actually kind.