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The child can either, take away the lesson that doing wrong will result in being punished, or they will take away the lesson they can hit things. I personally think the first lesson (doing wrong, or what mummy doesn't want you to do) will result in a spanked bottom will overlook the second, because a kid knows he's not allowed to hit other kids, so in doing so, he will be punished by a spank from mummy.
People are saying spanking leads to mental illnesses but also saying it leads to a violent child? (not you pixie i know) but it has to do with the lesson the kid learns. What he will learn, is to not wind up mummy.