In a category with fiber products, a morphism $Y\to X$ is said to be strict epimorphism if the sequence is exact: $Y\times_XY\xrightarrow{p_1,p_2}Y\to X$, (here the first arrow should be a double arrow which means two parallel maps).
What is the motivation to define the concept of strict epimorphism?
(I read about it in Milne's Etale Cohomology 2.17, where he showed a faithfully flat morphism of finite type is a strict epimorphism)