Tiresias's reluctance is rooted in the awful nature of the truth and the understanding that little good can come from disclosing it to Oedipus.  The understanding that Tiresias possesses can only bring unlimited misery to Oedipus, and the reluctance to come clean with lies in this idea.  It is one of the first moments where the theme of knowledge being a form of suffering is demonstrated in the play.  Oedipus demands to know the truth, and in this process, the prophet understands how painful this will be.  His reluctance to disclose it is testimony to this idea.  Only being after goaded by Oedipus with charges of disloyal does he disclose the awful truth.