This is a jukugo word that uses the on'yomi readings of the kanji. You haven't learned this reading for 織 yet, so here's a mnemonic to help you:

While you're spinning and weaving you are always absolutely shocked (しょく) by what you make. You never really know when you start and then BAM! You made elephant slippers. That's just how it works and it shocks you every single time.