Origins
To reject is to throw back.βββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββ The word comes directly from Latin reiectus, the past participle of reicere β from re- ('back') and iacere ('to throw'). The physical gesture is preserved in the word: something is offered, and you hurl it back.
Latin iacere produced one of the most systematic word families in English, where each prefix specifies a direction of throwing. Inject: throw in. Project: throw forward. Eject: throw out. Subject: throw under. Object: throw against. Trajectory: the path of something thrown across. Adjective: thrown towards (a noun). Even jettison and jet descend from the same root through French.
The word entered English in the 15th century, borrowed directly from Latin rather than through French. Its earliest uses were physical β rejecting an enemy's assault, throwing back an attack. The abstract sense of refusing an idea or dismissing a person developed quickly.
Figurative Development
Modern medicine gave reject a new domain: organ rejection, where the body throws back transplanted tissue. The metaphor is accidentally precise β the immune system treats foreign tissue as something hurled at it and hurls it back.
The noun reject (stressed on the first syllable) appeared in the 16th century for a person or thing that has been thrown back β refused, discarded, deemed unfit.