[Etymonline for 'propagation (n.)'] ... from propago (genitive propaginis) "that which propagates, offspring," from pro- "forth" (see pro-) + * pag-, root of pangere "to fasten" (see pact).

[Etymonline for 'propagation (n.)'] ... from PIE root * pag- "fix, join together, unite, make firm" ...

I heed the Etymological Fallacy. But what are some right ways of interpreting the etymology, to make it feel reasonable and intuitive?

How did pro- + PIE root pag- combine to mean the modern definition of 'propagation'?