As a kid, reading aloud in class was always nerve wracking because of this. The game was to do these double-takes so quickly that nobody could tell you were doing all of this extra work. Often you read ahead of what you're saying so that you can double-take before saying the word.
Yup, reading out loud was the absolute worst. I have different issues though, and because of my reading's tight associations with speech(1), I couldn't even read ahead. I think my "only-when-read-out-loud" stutter comes from the social anxiety I developed here.
(1) i.e. To read words with my eyes, I have to mentally speak them to myself.
It's not just your brain. It's how vision works in general. Everyone has physical blind spot (where the optic nerve attackhes to the retina) but no one can see it except if they carefully hunt hor it. Everyone can see high resolution only in a tiny area at the center of the visual field, and imagines the rest.
With dyslexia (and various physical vision problems), you're collecting even less input (due to misprocessing at some "lower layers"), so your higher-level recognition/comprehension brain has to fill in more missing deails, and so has a higher error rate.
An algorithmic analogy I would use would be fuzzy matching. Most people's brains are set to look for exact matches (or fuzzy matching with a super high match criteria). When one part of their brain needs access to a word, the other part of their brain will supply the exact match. My brain is using fuzzy matching with the confidence level set mistakenly low. When part of my brain needs a word, the first match returned is occasionally a false positive match. The rest of my brain just accepts it and continues onto the next requested word. The match quality isn't a traditionally fuzzy matching algorithm like Levenshtein distance. It is heavily weighted to both the start of the word and the expectedness of the word in the given context. The latter makes it very difficult for me to immediately notice my own written mistakes since I am already primed to expect what I intended to write and not necessarily what I actually wrote.
I seem to be able to break the spell in a number of ways. When I'm re-reading a final draft of something (say an important email) I will try to eliminate context and deliberately read each word individually. Another way to break this spell is to read a document much later in time. Sometimes the pattern matching self-corrects later, or seemingly I have forgotten the verbatim phrasing of the idea that I previously wrote, and so upon reading I pick up the mistake.
I read thousands of words per day, probably write well into the hundreds. Fortunately, the amount of errors for me is very low, but if this were to happen with increased frequency, reading and writing would be quite stressful.
For me personally, I have no problem with letters. A "b" is never a "d" or whatever stereotypical explanations you might hear about dyslexia. My problem is with entire words. I will often substitute one word for another while reading (and writing). I can go back and might still read that incorrect word. But I don't think I ever really "see" that incorrect word. It is more that my brain is lazy and isn't actually reading, it is just assuming what is supposed to be there and that assumption is occasionally wrong.