To draw a part out of a whole. What is taken keeps its meaning; what it was taken from is left changed.
Latin extrahere, ex- (out) plus trahere (to draw, to pull); the verb moved from the physical pulling of one thing free of another, a tooth or a splinter, to the more general drawing of any part out of any whole, including a fact out of a record.
Its root is the pull that once meant working a tooth or a splinter free: something held fast, loosened by force rather than handed over. What is extracted keeps the shape it had while it was still held, and the whole it came from keeps the gap.