A Discordant Piece of Cheese

My step-mother used this phrase once, "He's a discordant piece of cheese in many ways". There was a moment of silence and my sisters and I burst out laughing. What a great phrase. It was one her father used, I think. I get the discordant part, he was contrary, incompatible. But what's with the cheese part? Is a discordant piece of cheese the one on the plate that doesn't get along with the others? Or is it the one that in incompatible with the meal? Anyway, we are all discordant pieces of cheese in our own ways, neh?