pull out
繹 centers on drawing something out in a continuous, unraveling motion: pulling out threads, extracting meaning, or teasing out a sequence.
繹 combines 糸 (thread) with 睪, which likely contributes the sound and the idea of drawing out or unraveling. The exact historical development of 睪 is uncertain, but the phono-semantic structure is clear.
The left side is thread 糸, and the right side 睪 looks like a hand pulling something apart. Imagine pulling a thread to unravel a tangled knot, drawing it out bit by bit.
For エキ, picture pulling out a long, sticky thread of liquid from a bottle of extract: extract -> エキ, and the thread comes out smoothly.