An example of how people think about language would be explaining archaic usages that have survived in formulaic verses, prayers, etc. as something other than earlier forms. The nursery rhyme “Pease porridge hot, pease porridge cold” is easily explained by a reinterpretation of the singular noun “pease” as a plural and a mass noun. Its use as a singular noun is seen by comparing the way we might make up terms for porridge made from other items, e.g. carrots: carrot porridge, not *carrots porridge; cabbage porridge, not *cabbages porridge; and so forth, showing that when the nursery rhyme was composed, “pease” was still felt to be a singular noun.
Now I lay me down to sleep is an old middle voice form easily recognizable for students of other languages as a reflexive, i.e. I lay me down rather than I lie down. Of course, this is now made all the more confusing by the falling away of the distinction between the verbs “lie” and “lay”.
What people will do, however, is explain these forms as mistakes, e.g. I lay me down might be labeled baby talk. The rule for compounds where singular nouns only can be used is disregarded or, more likely, unknown to the armchair language mavens, and it is just assumed that the word is really peas but just misspelled or spelled in an archaic way. The idea of going to reference works on etymology is way beyond these folks, but pontificating on word origins is not, no matter how far off base they are. They therefore promote off-the-top-of-your-head etymologizing along with other bizarre formulations to explain language, contributing to the notion that language doesn’t make any sense or, worse, that only “perfect” languages like Latin make sense while English is just a hodge-podge of errors and malapropisms whose speakers need more rules to keep them from falling into a state of “incommunicado”.
These off-the-cuff attempts to explain language are called “folk etymologies”.