Please explain, "Asymmetric is stronger than simply not symmetric". In some textbook I found a statement like, "Asymmetric is stronger than simply not symmetric".
But as I try to perceive this statement, both appear to be same to me.
For example, parentof is an asymmetric relation. If $A$ is a parentof $B$, $B$ can not be parentof $A$. We arrive at the same conclusion if we call this relation to be not symmetric.
(Liyang Yu. A Developer’s Guide to the Semantic Web.
2nd. Springer, 2014. p 226, last sentence of second paragraph from bottom.)

In asymmetric and antisymmetric relationships no two distinct elements can be joined by arrows in the two directions. Moreover in asymmetric relationships there can be no loops.
Partial orders are antisymmetric. Strict orders are asymmetric.
Both conditions are generally different from the negation of symmetry; the latter means that there is at least one pair of distinct elements with an arrow in one direction but not the other.
