[davem]

'Hope on then!' laughed Denethor. 'Do I not know thee, Mithrandir? Thy hope is to rule in my stead, to stand behind every throne, north, south, or west. I have read thy mind and its policies. ... So! With the left hand thou wouldst use me for a little while as a shield against Mordor, and with the right bring up this Ranger of the North to supplant me. 'But I say to thee, Gandalf Mithrandir, I will not be thy tool! I am Steward of the House of Anarion. I will not step down to be the dotard chamberlain of an upstart. Even were his claim proved to me, still he comes but of the line of Isildur. I will not bow to such a one, last of a ragged house long bereft of lordship and dignity.'

Therefore later, when all was made clear, many believed that Denethor, who was subtle in mind and looked further and deeper than other men of his day, had discovered who this stranger Thorongil in truth was, and suspected that he and Mithrandir designed to supplant him.

Clearly Denethor recognises that Gandalf has both power & authority. He probably also acknowledges that he is a 'steward'. The point is they wanted different things. Denethor wanted things to remain as they had always been during his lifetime. Gandalf wanted to reinstate the kingship of Gondor under Aragorn. Denethor refused to acknowledge Aragorn's right to rule: 'I am Steward of the House of Anarion. I will not step down to be the dotard chamberlain of an upstart. Even were his claim proved to me, still he comes but of the line of Isildur. I will not bow to such a one, last of a ragged house long bereft of lordship and dignity.'

What he's saying is that he doesn't care if Aragorn is the Heir of Isildur, - he will not accept Aragorn's rule. So when Gandalf tells him ''To me it would not seem that a Steward who faithfully surrenders his charge is diminished in love or in honour,' it is obvious they are at cross purposes. Gandalf's position is that Denethor's duty is to surrender his rule because the true king has returned, Denethor's is that the true king has not returned, as the 'true' king would be the heir of Anarion, not of Isildur. Denethor could not accept Aragorn as king so he could not surrender his office to him because that would (in his mind) be a betrayal of his duty, which is to rule Gondor till the 'true' king returns.