Desdemona brings shame upon her family due to her relationship with Othello. She also did not ask her father for permission to marry. Due to the context, Desdemona has been raised to believe that bringing shame upon her family is one of the worst things that she could have done as it takes away from her chaste image, expected of woman at the time. This would evoke a lot of fear. For most women in wealthy families, shame would be the worst possible outcome.