Making it a flaw in logic is difficult. A common approach is to have the character trying to work something out, and they notice an object which gives them an (an obviousobvious) solution. e.g. they want to get on the roof, they see a ladder. But then, after they leave, we zoom in on the ladder to reveal some detail not visible to them e.g. a splintered rung or loose nail. Dramatic chord!
But that's ignorance, a flaw in knowledge, not in reasoning. The problem becomes "how to show a splinter in logic, not in a ladder?" How do you show logic, at all? In the below, I suggest ways of showing general lack of logic, and how to show a specific lack of logic.
Note that general or specific irrationality does not necessarily mean stupid (just as clever does not necessarily mean wise). Cue mad scientist.
Related is suspension of disbelief: in accepting the conceit of a story, readers willingly accept the illogical, counterfactual, improbable, implausible, impossible. Talking animals, superman, ghosts, eerie supernatural guidance and justice. Even readers who notice a plot hole or inconsistency will often allow it, in order to enjoy the story..
General So, apart from very specific reasoning, you just need to make it more plausible that the character has flawed logic - that that explanation is primed to be the first thing to enter the reader's mind, by showing the character to be illogical, neurotic, irrational in general.
Some blunt examples: have the character do cliche neurotic things to establish their illogical nature: like OCD checking everything twice, unnecessary rituals, paranoia. So, now when their plot-significant actions come up, the reader will be ready to suspect it's a bit crazy. But here's the danger: there's a common trope where setup is used to show their neutroticism was justified all along! (Because readers willingly suspend belief). However, maybe that's OK for your question, as they're not seeing it as an authorial error.
You could also establish the background history of their erroneous thinking: an experience making them irrationally fear something ordinary... and when it comes up in their plans, they make irrational allowances for it,
Specific Similarly, you could show their specific error in a minor scenario, perhaps one presaging the main plot. But this I think is really tricky: if they make this error, and they fail because of it, why don't they learn from it? I suppose you could just show them making the same error time and again, and that would be enough to prime the reader for it to happen again (and the "why" is just secondary background).
Alternatively, if they make this error, and it does work out but clearly for some other reason (so they don't learn), the reader might take the message that they are magically lucky, and it's something they can and do legitimately rely on. But again, for your question, this again might be OK, because it's not interpreted as authorial error.