Mishna: An egg which is laid on Yom Tov: Beis Shammai: It may be eaten. Beis Hillel: It may not be eaten.
Rav Nachman: The egg is muktzeh.
Rabbah: The egg is forbidden because of Hachana.
Rav Yosef: The egg is forbidden because of gezeiras peiros hanoshrin.
Rav Yitzchok: The egg is forbidden because of gezeiras mashkin shezavu.
The others (Rabbah, Rav Yosef and Rav Yitzchok) do not explain the Mishna like Rav Nachman because of our kasha (003) [the Mishna could have easily taught both laws “Beis Shammai permit the chicken and its egg”?].
They do not explain the Mishna like Rabbah because Hachana is a novel idea which they don’t hold by.
Question: Why does Rav Yosef not give the same reason as Rav Yitzchok?
Response: An egg is a solid food and is more similar to peiros.
Question: Why does Rav Yitzchok not give the same reason as Rav Yosef?
Response: An egg is concealed within the hen and is more similar to wine that is concealed in the grapes.
Rabbi Yochanan was active in Eretz Yisroel soon after Rav Yitzchok.
Rabbi Yochanan also explained the Mishna in terms of a gezeiras mashkin shezavu [like Rav Yitzchok]. This is implied by the question and answer which Rabbi Yochanan said in explaining Rabbi Yehuda’s position, as shall be explained:
Mishna: One may not squeeze fruits for juice on Shabbos or Yom Tov [as Tosfos explains, that although preparing food is permitted on Yom Tov all melachos up to lisha are prohibited, and juicing is included in Dosh - Threshing], if juice flowed from grapes and olives without being squeezed, the juices are forbidden.
Rabbi Yehuda: If they were prepared for food, their juice is permitted, if they were prepared for juicing, the juice is forbidden.Rabbi Yochanan: So we see that according to Rabbi Yehuda, anything that comes from something prepared for food is consider like “a small piece of bread that was removed from a loaf”.