Valentine is upset when her father starts reading and agreeing with Demosthenes because Valentine "didn't like some of the positions Peter made Demosthenes take" (136). Demosthenes is described as a "paranoid anti-Russian writer" (136). He uses fear tactics to gain an immediate audience and starkly contrasts the more conservative and thoughtful Locke. Demosthenes does not actually represent any of Valentine's opinions and is far too irrational. This is done so that Peter and Valentine must rely on helping one another (and using each other's ideas) in writing for each pseudonym. Because she does not necessarily agree with Demosthenes, Valentine must work harder and think through her writing even further.
The result of this approach to the arguments is that Demosthenes gains followers very quickly and is noticed and respected before Locke. Valentine is annoyed at how easily and quickly the reading audience is persuaded. Valentine actually thinks most of Demosthenes' ideas are foolish and that only "fools would follow him" (138). She is disappointed to find out her father is one such fool.
Valentine herself doesn't believe what "she" is writing. Its all fear mongering propaganda to set the stage for Locke--the one whose ideas she actually supports. The fact her father, who is quite an intelligent man, can support such ideas upsets Valentine. Valentine is appalled that her father could agree with such "nonsense".