[Formendacil]

I don't think that Tolkien ever clearly explained it, but I should say that it has a great deal to do with Aragorn.

Aragorn and Gandalf were clearly associated. It says, in the Appendices, I believe, that when Thorongil came to Gondor, Ecthelion began to listen to Gandalf's counsels more than he previously had, and Gandalf became a greater factor in the Gondorian scheme of things.

Considering Denethor's dislike of Aragorn (based on the usurption of his father's affection and his thread to Denethor's status), it is easy to see that he would dislike Gandalf as Aragorn's partner.

Also, in later years, as Denethor used the Palantir, I imagine he did more than just look at the growing Ork armies. He would have been keeping tabs on Gandalf, and others (although I imagine that Aragorn was not one that he managed to keep an eye on, considering the number of years between when he left Gondor and when Denethor started using the Palantir. That and his changed status...)

And, as Denethor says before his death, he knows that Aragorn is coming from the north, and that Gandalf is associated with him. Since he talks about the "ranger from the north to supplant me", he obviously knows that they are connected, and that Aragorn is coming for the throne eventually. He's probably known this for quite some time.

And, Gandalf is well known as persuader/manipulator. I think it's very easy to see why Denethor dislikes him.