Denethor vs. Aragorn

[Belegorn]

I should mention that like I said Denethor's view was one that was held a long time since just before the North Kingdom fractured. The council of Gondor told Arvedui, the King of the North, "The crown and royalty of Gondor belongs solely to the heirs of Meneldil, son of Anárion, to whom Isildur relinquished this realm. In Gondor this heritage is reckoned through the sons only;" [RotK, Appendix A] This is imo the reason why Denethor would not see Aragorn as a rightful heir, or at least he'd use this as a reason.