c. 1300, "an exit," from Old French issue "a way out, a going out, exit; final event," from fem. past participle of issir "to go out," from Latin exire "go out, go forth; become public; flow, gush, pour forth" (source also of Italian uscire, Catalan exir), from ex- "out" (see ex-) + ire "to go," from PIE root *ei- "to go."
Meaning "discharge of blood or other fluid from the body" is from 1520s; sense of "offspring, children" is from late 14c. Meaning "outcome of an action, consequence, result" is attested from late 14c., probably from this sense in French. Meaning "action of sending into publication or circulation" is from 1833.
Legal sense developed from the notion of "end or result of pleadings in a suit (by presentation of the point to be determined by trial)," hence "the controversy over facts in a trial" (early 14c., Anglo-French) and transferred sense "point of contention between two parties" (early 15c.) and the general sense "an important point to be decided" (1836). Hence also the verbal phrase take issue with (1797, earlier join issue, 1690s) "take up an affirmative or negative position in a dispute with another." To have issues "have unresolved conflicts" is by 1990.