Old English guttas (plural) “bowels, entrails,” literally “a channel,” related to geotan “to pour,” from Proto-Germanic *gut–, from PIE root *gheu- “to pour.” Related to Middle Dutch gote, Dutch goot, German Gosse “gutter, drain,” Middle English gote “channel, stream.” Meaning “abdomen, belly” is from late 14c. Meaning “narrow passage in a body of water” is from 1530s. Meaning “easy college course” is student slang from 1916, probably from obsolete slang sense of “feast” (the connecting notion is “something that one can eat up”). Sense of “inside contents of anything” (usually plural) is from 1570s.
To hate (someone’s) guts is first attested 1918. The notion of the intestines as a seat of emotions is ancient (see bowel) and probably explains expressions such as gut reaction (1963), gut feeling (by 1970), and compare guts.