It has to do with whether it's treated as a substance or as an object. Most nouns are either one or the other: 'chalk' and 'water' are substances (you can't say 'a chalk' or 'a water'); 'piece' and 'body' are objects (so you can say 'a piece of chalk' or 'a body of water', but not 'it was full of piece,' or 'I was covered in body').

'Shit' can be used either way. So we can talk about 'a shit' when we mean a particular turd, or just 'shit' when we're talking about the substance.

"That's bullshit" and "He gave me shit" = shit as a substance
"I don't give a shit" = shit as an object (still a weird way to phrase it)

There are still odd things about colloquial phrases like those, though. How about, "I took a shit." Shouldn't it be, "I left a shit"?

It's weird, but 'sweet' is the opposite of almost every other kind of taste. Bitter - sweet; sour - sweet; salty - sweet.