Those visual illusions are physiological, not cognitive
Have you seen those visual illusions that are used as analogies to explain why human cognition distorts the facts? Here are some notes relevant to that sort of argument.
It's useful to distinguish senses of the word 'see' that refer to visual sense products, sense products in general, their interpretation (for example, as evidence of a specific claim), an understanding of another's opinion (in particular, their "perspective"), and an agreement with another's conclusions.
Consider that even if someone were to see another's perspective, that would not require agreement with that perspective or acknowledgement of the fact even when that agreement secretly exists.
We cannot choose our internal experience of our actions and instead can only anticipate them with limited reliability. Our cognition is a navigation of both an internal and an external set of situations. In addition our information processing involves a mix of observations, memory, and imaginations. As a consequence, planning of personal experience is also prone to failure because of the information processing on which it is based.
Introspection and claims of personal beliefs can be false whether or not a person intends to deceive themselves or others. This complicates gathering evidence of cognitive functions and actual beliefs held by others. Easy examples of cognitive failings are suspect.
As an aside, there is personal ignorance, the measure of our epistemic limitations compared to a hypothetical omniscient's knowledge. I believe human cognitive failings are due to limitations of one's knowledge, memory, imagination, and attention (on external and internal experience). Those four limitations cause our ignorance of the truth.
Something like emotion or belief could be part of the set of internal experience and can serve as a reason in planning what you experience but only through its effects on memory, imagination, or attention.
Whether truth is remembered or inferred, error in conclusions is a mismatch to a truth that is assumed rather than directly known, a truth that is an omniscient’s view of reality. Thus interpersonal agreement is not a proxy for the truth and the cognitive limitations of others cannot be decided on the basis of their disagreement with a consensus.
I am not interested in the particulars of evidence procedures or models here though a discussion of their application in context would clarify that the term “true” can mean “useful” in some conversations.
All to say that while visual illusions are illustrative of errors in conclusions, they are not examples of those errors. Your eyeball does not do all the information processing for your brain.
You can see that I reject conventional ideas of cognitive errors here. However ideas like the Dunning-Kruger effect are useful in some contexts (for example, during introspection when you have accurate access to your own beliefs and memory of your own behaviors and motives).