Shit for brains actually come from the custom of Latvians who, at one time, used fecal matter to stuff a dead bodies crainial orifices before burial. This was an inexpensive method of getting rid of a lot of shit and saving a few bucks.
However, during WW2 GI Joes serving in Europe misunderstood the references and took it to mean an insult.
They began using the saying at home in the USA

An idiot; one who seems to have shit instead of brains, thus severely limiting their thought capacity.

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Shit-for-brains is commonly used to describe people who often go off topic and talk about something completely irrevelent. These people aren't very good at socializing and are extremely random. (most likely they are trying to acheive a certain kind of humor but failing miserably) Also see dumbfuck