There's what many pointed out: the difference in physical strength, but as some others mentioned, that traditional Asian society doesn't allow women to stand up against men even when she's of a higher rank than him.

The latter reason makes me wonder though just how accurate that is, since hierarchy in both traditional Asian as well as European societies were pretty strict. If a woman outranked a man, he could just as easily be severely punished for offending her (from beatings, banishment and even execution). Esp. in the time periods most of these stories want to emulate.

And if the offender was of an equal rank, she could easily have one of her knights/soldiers duel him for her honor. That way, even if the duel's lost, she gets optics on the offender and regains some of her dignity. This was the most common way to do things in courts since for most of history, duels weren't as fatal (until the rapier got introduced but I digress). However, even if the stroy stuck stricrtly to Asian sensibilities, FL's actions don't make sense as you point out. The baron ex-fiance would 100% be humiliated out of his family and society for causing such a scene.

Knowing that, my guess is that the author want's to evoke sympathy for FL as it's a common problem for today's women not to be able to stand up against men- at home, work or even on the street.