One of the reasons that Tony is hesitant to take on the role of mentor with Peter is because of Obadiah Stane.
We all know that Tony has a hard time trusting anyone and that he genuinely does care about Peter. But Obadiah’s betrayal not only as a business partner, father figure and mentor just shattered his faith in himself in that role for Peter.
Setting aside everything that happened with the Avengers in the Civil War, Tony really does care about Peter and taking on the role of mentor and defacto father figure scares him not only with Stane’s betrayal but Tony’s own lack of connection with his own father, Howard. So him embracing this role not only will help him heal from CW but helps him get passed Stane’s betrayal and Howard’s lack of parenting, and shows Tony that he can be that person that people can rely on not just as a teammate but as family.