Is the girl considered sinful for her stubbornness and arrogance, and is the husband sinful for abandoning her until she requests a divorce, and is she considered disobedient by her desertion of him?

After the marriage contract, she becomes your wife, and it is permissible for you both to communicate and exchange feelings. Her lack of interest may be due to shyness or societal norms. Do not rush into divorce; instead, communicate with her and her family to understand the reason for their unwillingness to proceed with the marriage, as it might be due to what you mentioned to her mother about preferring separation. Do not consider your wife disobedient (nashiz) for not communicating with you, because her obedience before consummation is to her guardian, not to you. If she requests a divorce without a valid Shar'i reason, you have the right to refuse until she pays you a compensation (khul'). If it becomes clear that there is an impediment to the continuation of the marriage, divorce before consummation is easier. Arrogance is blameworthy; it is "rejecting the truth and belittling people," and it is not permissible to practice it, whether with you or not.