How we cite our quotes: (Line)
Quote #1
Or the nursemaid,
some luscious sweet from Denmark
who captures the oldest son's heart. (6-8)
The key line here is the second one, which characterizes the nursemaid as a "luscious sweet"—kind of an objectifying term, if you ask us. It turns the woman into something for consumption, and the "some" makes her just one of many, as if her individuality didn't matter. Moreover, it seems that her "sweetness" (in terms of looks, not personality) is the only thing that gets her ahead.
Quote #2
Next came the ball, as you all know.
It was a marriage market.
The prince was looking for a wife. (41-43)
The whole "marriage market" thing is possibly one of the most cynical moments in the whole poem. It portrays the women at the ball as mere objects for a man to choose among. Women here, as a gender, can do nothing more than to marry into money. There's certainly no implication that they could get ahead on their own.
Quote #3
Now he would find whom the shoe fit
and find his strange dancing girl for keeps. (77-78)
The important phrase here, we think, is "for keeps," an expression that implies eternal possession. Prior to this passage, the prince has covered the steps of his palace with wax in order to try to trap Cinderella—or at least, her shoe. (This sounds more like a trap for an animal than a girl, right?) So he gets her shoe and then basically thinks "Okay, now I've got her for good." It's not exactly the most romantic thing in the world, when you think about it. Cinderella, as a woman, is again being seen as a kind of object.