Why does Cole thinks his dad agreed to pay for all the expenses of the banishment?

Cole believes his dad agreed to pay for all the expenses of the banishment as a way to alleviate his own guilt and responsibility for their troubled relationship. By financially supporting the process, his dad may feel he is making amends for his shortcomings as a parent. This action reflects a desire to distance himself from the emotional aspects of their connection while still trying to be involved in Cole's life. Ultimately, it highlights the complex dynamics of their relationship and the challenges they face in communicating and understanding each other.