I understand this sentence, but when I dissect it, I realize I'm not sure why に is being used. Does anyone care to explain?
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Welcome to the site! I'm new, too. (For me it's more about old shoes than hats; when your feet get used to them, it is hard to throw them away no matter how much your wife is yelling...)
In general, the sentence was a bit clumsy, I think, but AFAIK the に is used correctly. (=She wants you to be the person to throw it away). I don't know about your Japanese skills, so, allow me, we need to get used also to illogical structures, esp. when seen from the English point of view). I mean, I have still difficulties even to accept that AはBに勝った is OK...