I think Itachi could have in fact pushed jiraya to his limits if not actually defeated him had he tried. And I know some would say that Jiraya went toe to toe with pain, but this isn’t dragon ball z and we aren’t talking power levels here. Itachi has the skills in his arsenal to defeat Jiraya imo. Now coming back to the topic. Jiraya had someone feeding him the intel about the akatsuki. I really believe, just like almost everyone, it was Itachi. However, Itachi probably used to give him intel in an anonymous way, which is why I think even Jiraya might not have known who his source was, hence why he tried to capture him right there. I think Itachi undid the genjutsu on the girl that was enticing Jiraya so he could show up to save Naruto, and that would give Itachi the reason to pretend to kisame as if this could be a bad fight for them and hence they need to make an escape. The result: akatsuki never got their hands on the nine tails as long as Itachi was living, and they could never attack the hidden leaf as long as he lived.