The ML has trouble saying that he loves the FL, and the FL won't go through with a marriage without reciprocated love, especially not to a man of such a high position (marrying a duke is no small thing for the FL who is from the country and rather low in the hierarchy). So, the FL acts as if she'll break the engagement in order to spur the ML on, which while rather manipulative is 'good' in the long run as by doing this she ensures that they 1) marry while being completely certain they love eachother and 2) in such a way that makes sure that their future married life is one free from malicious rumors such as "it was arranged by the prince, they don't actually love eachother". The FL is a lot more politically savvy than she is kind-hearted.