Coequalizer of a reflexive pair from a pushout

For a reflexive pair $f,g:A\rightrightarrows B$ with common section $r$, form the pushout in a category of $f$ and $g$, with maps $j_1,j_2:B\to P$. The equation $j_{1}f=j_{2}g$, composed with $r$, gives $j_1=j_2=q$. This common map is a coequalizer of $f,g$: every map equalizing them defines a commuting pair into the pushout and hence factors uniquely through $q$.