Then Pilar needs to work on refining her sense of what's an allowable argument until Keltham stops sounding persuasive about the fish thing. Either that, or accept that humans actually are fish.
Pilar should - hopefully - be able to notice something stretched about the way that Keltham said very loudly and sternly that anything which was naturally born to two fishes mating, without magical interference, would by definition be a fish. She should, hopefully, be able to notice a stretched feeling inside her mind, considering that. If she can't, yet, note it down, accumulate a bunch of those things, and review them with an Owl's Wisdom after the lecture is over.
In the future, noticing something stretched like this, when Keltham isn't pointing directly to it, will probably manifest as Pilar noticing a quiet note of disquiet in the corners of her mind. She should maybe hit herself with an Owl's Wisdom as soon as she has that first experience, it's a really important one to remember and recognize and learn to feel explicitly and consciously every time it happens.
This is not about despair in how reasonable arguments can reach wrong conclusions. This is about your own sense of what is 'reasonable' being broken. This is about taking more Validity into yourself. This is about using the styles of cognition and kinds of arguments that make it easier to argue for true things than for false things.
But even ilani, when they stretch themselves to their limits - possibly even Keepers - cannot be sure of what is and isn't valid, when they are doing deep thinking not in numbers and stretching their intuitions to their limits. So they learn, first to reason validly, but also, not to let themselves flinch towards or away from thoughts, not to let their minds go to looking for arguments for a bottom line already written; only to wonder "Is X true?" and not "How do I argue for X?"
If Pilar is starting to doubt lots of argument steps and see possibly fallacies everywhere, and feel unsure which arguments are valid - she'd better rush to master the art of evenhandedness and purifying her cognition from flinches. Otherwise, those doubts-of-validity and arguable-fallacies will, perhaps, arise swiftly when Pilar considers something she doesn't want to believe, but seem more distant - just not come naturally to mind - when she is considering something she wants to believe.
If you are swifter to look for flaws and fallacies and invalidities in incongruent thoughts, than in congruent thoughts, then learning more about the Art only makes you that much stupider; it gives you that much more spellpower with which to blast down everything you don't want to believe, all the arguments you don't want to accept, and keep your bottom line in place forever.
Of which it was said out of dath ilan: Intelligence, to be useful, must be used for something other than defeating itself.