Thinking about Denethor, I realize that he may have had the same problem with
his father Ecthelion II that Faramir had with him. Ecthelion II's favorite captain was Thorongil ("Eagle of the Star").
Denethor II was a proud man, tall, valiant, and more kingly than any man that had appeared in Gondor for many lives of men; and he was wise also, and farsighted, and learned in lore. Indeed he was as like to Thorongil as to one of nearest kin, and yet was ever placed second to the stranger in the hearts of men and the esteem of his father.
It must have really stuck in his craw to find out that Thorongil was the rightful king!
I remember Denethor's inacition being a result of his having been decieved (by Sauron) as he looked into the Palantir. I see him as being concerned mainly with power and the exercise thereof. Ultimately, like the Democrats, his concern for power outweighed his concern for country.