Well the thing is, the engagement involved the other party family member. Even if the father want to cut off the engagement, he can't just say "My daughter dont want to get married, and want to live a slow life in a countryside." So easily. I bet the other noble family member wont like that decision after agreeing to married their son to his daughter after the father, which is the one who suggest that. And it could lead to potential war or conflict for the nobles that got involved (lotus, and i forgot).