Why do you think that is?
Is it that Europeans see eating out as a signal of luxury and asking to take the rest of the food home somehow diminishes that perception ("oh look they must be poor if they are taking that left-over steak home..." kind of attitude). In other words are Europeans just afraid of looking bad, poor or stingy in front of others in a restaurant and Americans just don't care?
What if portion size wasn't a problem? Image that Europeans served same sized portions as Americans, would you take your leftovers home to be heated up for lunch then?