Well for someone who hasn't studied Tolkien for long, that's a very original and I think valid point! Denethor must have been insecure to have felt threatened by Thorongil in the first place. He should have just known that his father would always love him more than this stranger, just as he had no real reason to be threatened by a popular captain [except of course that he did!].

And yes, that's exactly who Sauron works. He exploits existing weaknesses and unfortunately he did a good job on Denethor.