The story
From a likening of the vagina (especially one enlarged by childbirth) to the stereotypical billowing sleeves of a wizard's robe. Note Russian не прише́й пизде́ рука́в (ne prišéj pizdé rukáv), which puts the same two elements together, but in an absurd way, not comparing them directly.
Etymology from Wiktionary, CC BY-SA 4.0.