Is it permissible to withdraw from completing the marriage after the marriage contract has been drawn up (katb al-kitab) if the spouses differ and there is no compatibility between them?

If your paternal cousin is upright in his religion and character, do not rush to seek separation, for many disputes can be remedied. The most important thing is his relationship with Allah Almighty, because he helps his family obey Allah and is trustworthy. However, if he is negligent in his religion, then leaving him is better. You should perform the Istikhara prayer and consult your righteous family members. Strive to adorn yourself with the best qualities, for the flaw might also be from you.

As for the saying: "Destiny willed it," it is a common mistake. Destinies have no will. The correct statement is to say: "Allah willed it" or "Allah decreed it," because will is intention, and a description has no will; rather, the will belongs to the one described.