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.)

If a relation is symmetric then there is a two way arrow, e.g. if someone is a blood relative of me then I HAVE to be a blood relative of them.
If a relation is not symmetric then there can be one arrow or two, e.g. if I like someone then they may or may not like me, either case could be true.
If a relation is Asymmetric then having one arrow means that there definitely cannot be two, e.g. if someone is my parent then I definitely CANNOT be their parent.
So basically the difference between non-symmetric and asymmetric is that in one we might have two arrows some of the time, but in the other we can NEVER have a second arrow once we have the first.
