Why is the antonym of "within" not "without"

Solution 1:

As an antonym of within, without is an archaic, literary form:

outside (prep.):

  • "the barbarians without the gates"

outside (adverb):

  • "the enemy without"

Without:

Old English wiðutan "outside of, from outside," literally "against the outside" (opposite of within), see with + out (adv.).

As a word expressing lack or want of something (opposite of with), attested from c. 1200. In use by late 14c. as a conjunction, short for without that.

(Etymonline)