When $g \circ f$ is an extremal monomorphism, $f$ must be an extremal monomorphism. Why?

Question

I couldn't prove part (2) of the proposition 7.62 in Adameck's book (Abstract and Concrete Categories: The Joy of Cats). It states that if $g \circ f$ is assumed to be an extremal monomorphism, then the rightmost morphism, $f$ must be an extremal monomorphism too. I could not prove it. Is there any straightforward proof?

Thanks very much,