I found "non si insegna a nuotare ai pesci" in several books about Italian proverbs, so I think that's it
I also found
l'uovo vuol sapere più che la gallina
l'uovo vuol sapere più della gallina
l'uovo ne vuol sapere più della gallina
These seem to be variations of, more or less, "the egg wants to teach the hen." It looks like it might be old fashioned. "The eggs do not teach the hen" turns up as a Russian proverb. яйца курицуне учат A book on Russian culture translated the proverb as "don't teach your granny to suck eggs" (followed by a lateral translation).