But 'seinen' refers to 'he', 'his' fish. 'Her' fish wouldn't be correct, isn't it? The fish in this context must belong to a man, not to the girl ('ihren')
"sein" refers to "er" or "es". "The girl" is "das Mädchen", so it is "es" and "sein".
In fact, "No girl eats her fish" should be also accepted. In German girl = Mädchen = es, so in this case her (girl's) = sein (not ihr). I did not risk trying "her fish", though.
I tried. It works
I wrote "No girl eats his fish" and it was marked correct. An example of not assuming context during translation I suppose...
Why isn't this answer right? "A girl doesn't eat her fish"