How did 'ex-' + 'serere' compound to signify 'thrust out, put forth'?

Question

Etymonline avers the etymology for 'exert' to be from:

1660s, "thrust forth, push out," from Latin exertus/exsertus, past participle of exerere/exserere "thrust out, put forth," from ex- "out" (see ex-) + serere "attach, join" (see series). Meaning "put into use" is 1680s.

[ OED: ] [...] The formation is probably due to antithesis with inserĕre (to insert v.) [...]

ex- + serere literally signifies 'to attach or join out', which doesn't make sense. How did they compound to signify "thrust out, put forth"? How ought this compound be understood?

Answer 1

I may be misunderstanding what is exactly unclear here, so I am sorry if I am misinterpreting the question. The sĕro, sertus has the semantics of binding into a bunch: “wreath; join, entwine, interweave, bind together; compose; contrive;” [Whit.] (There is also an irrelevant lemma of sēro).

in-serere, with the regular semantics of in-, directs the action of the verb inward, giving it the force of bundling in, adding to the bunch, wreath or bundle: “to put, bring, or introduce into, to insert” [L&S]

ex-serere, with the ex- expectedly directing the action outward, essentially means un-bundle, separate or protrude from, be taken away from the bunch: “to stretch out or forth, to thrust out, put forth, to take out; to protrud[e] from the dress, [to be] bare, uncovered” [L&S].