The symmetry of $\mathsf{Rel}$ is the natural isomorphism
\[ \sigma ^{\mathsf{Rel}}_{A,B} \colon A\times B \to B\times A \]
at $\webleft (A,B\webright )$ is defined by declaring
\[ \webleft (a,b\webright ) \sim _{\sigma ^{\mathsf{Rel}}_{A,B}} \webleft (b',a'\webright ) \]
iff $a=a'$ and $b=b'$.
