Re-reading the Lord of the Rings, Chapter 50

It is clear that Denethor, while initially being broken by failing hope and assumed bitterness as to shield him, now falls to pride and fear of humiliation and against his own best counsel, choosing callosity, but had he had any real hope for Faramir, he would not have done so, meaning that he has still good reason to assume that the war will be lost, but not anymore good enough to convince himself that what he's doing is commanded by Gondor's honour.

His final choice is to flee - in a very cruel way. He doesn't complicate Gondor's affairs with it though, taking his own life in this way, and only his own life, is pretty much a private decision and the truth is that the world, that Denethor has created around himself, is a world, from which all living things would eventually flee - yet he chooses not to break it for it is his life and pride.

Pride and honour often go hand in hand, but they are not the same, for pride springs from one's own contribution to honour and in becoming accustomed to it, one might forget her.