because her sister spread those rumors. I don't remember the context, but MC did slap her in public. Her sis probably took the chance to worsen her reputation even tho MC was not in the wrong, and as I understand that there is some superstition against red hair in the south as well. The family was using the sister as the advertising face for the events MC organized (likely bc MC had red hair), so public thought the sister was a good and pure person and that MC must be evil for arguing with her (bc the sister has too idealistic view of how nobility should act but little to no actual management skill).