this is disgusting, so the framing is that because a man will be embarrassed she should be a breeder, and just die instead of her sister....that's the joke.
Also the man is a Duke, He has higher status then everyone that why its called social status, he could have just said "he was thinking about proposing to someone" and that Emily misheard, on top of the fact that he has better social status, and far more finical standing then Dylan so he has power over her. He also knows she doesn't want marry him but he decided to force her into a situation anyway.