What advice can be offered to a girl who holds certain beliefs regarding the superiority of women over men, hatred of men, her interpretation of hijab, her support for secularism to obtain rights, and that cooking is a man's duty, in addition to her claim of pride in Islam and her endeavor to establish a "modern Islam"?

This girl has positive qualities, such as her pride in Islam and her commitment to it. It is important to differentiate between acceptable and rejected aspects of her ideas, as she is young and her thoughts are still developing and subject to change.

Her ideas regarding the preference for women and hatred of men: These are not religious beliefs but rather emotions and feelings that may change with experience and deeper understanding. Men and women complement each other to achieve high spiritual and moral dimensions. The existence of superiority in some women does not negate the fact that men, in general, are more capable of managing major leadership positions.

Her view of women's status in secular countries: This is due to her ignorance of Islam's high regard for women and her lack of awareness of the real figures and statistics concerning women's status in those societies, which reveal widespread incidents of harassment, rape, and sexual exploitation. A woman's body in the West is often exploited as a commodity.

Her view of Jihad: This is a mistaken view, stemming from her ignorance of the rulings and wisdom of Jihad in Islam. Jihad continues until the Day of Judgment and is a source of reward and gain.

The questioner is advised to guide the girl by directing her to this answer and to avoid direct conversation with her to prevent fitna (temptation/strife).