I haven't seen the raws but based on what we know so far, First Princess could be Tomboyish to great degrees especially during the fishing bout.
We are gonna assume she does not know what sex is, or what it can result to rather.
so, to her, this is dueling and she believes it will be a vow towards marriage between these two.
...
Even crazier might be, she thought she saw her parents were "duelling" on the bed at a younger age as a reason why she's doing this.