My simplistic thinking is that each person has one brain, so why do we say "blow someone's brains out"?
It's hard to say, since we've been doing it as long as the word has been around. The OED gives: I. Senses denoting organic structures. 1. a. The organ contained in the skull of humans and other vertebrates b. In pl. in the same senses. Now usu. as a mass noun, chiefly in Cookery.
?c1400 tr. Secreta Secret. (Sloane) 11 Many heres and softe signyfies buxomnes and coldnes of brains.
As for the comment about mass noun, note that you don't blow the entire brain out, just bits of it.
I see nothing at all wrong with @Brett Reynolds's excellent answer - I'm only really posting this to graphically illustrate that plural brains has always been as common as brain, even for one individual.
Maybe it's because if you actually look at a brain, it seems to be made of lots of bits (we certainly do the same with guts). Or maybe we think we're so smart the singular doesn't do justice to the organ.
Beats me, but etymonline notes:
The custom of using the plural to refer to the substance (literal or figurative), as opposed to the organ, dates from [the sixteenth century].