Question

why is a separating funnel narrow at the bottom

Answer 1

A separating funnel is narrow so that the mixtur which is going to be separated will separate and when the separation is over you close the tube by the tap

Answer 2

Separating funnel is used to separate out unwanted matter from wanted matter. So the narrowness of the bottom is useful so that the liquid falls down drop by drop and in a controlled manner to separate out impurities from the pure particles