Gemara

(Mishnah): We may not squeeze fruit to extract the juice. If the juice came out by itself, it is forbidden [on Shabbos].

R. Yehudah says, if the owner planned to eat the fruit, the juice is permitted. If he planned to extract the juice, it is forbidden.

(Shmuel): R. Yehudah agrees about olives and grapes.

(R. Yochanan): The Halachah follows R. Yehudah regarding other fruits, and Chachamim regarding olives and grapes.

(Rabah): R. Yehudah agrees to Chachamim about olives and grapes; Chachamim agree to R. Yehudah regarding other fruits.

(Rav Nachman bar Yitzchak): He holds that they argue about berries and pomegranates.

144a: Rabah learns from a Beraisa;

(Beraisa): We may squeeze plums, quinces and crabapples, but not pomegranates;

In the house of Menasiya bar Menachem, they would squeeze pomegranates.

Since these other species are not normally squeezed, one may squeeze them l'Chatchilah.

(Rav Nachman): The Halachah follows this Tana, for he holds like Menasiya.

Objection: Menasiya is not the majority of the world!

Answer: Indeed, the practice in one region can determine the Halachah everywhere!

(Mishnah - R. Elazar): If one lets cactus grow in a vineyard, this is Kil'ayim.

Chachamim say, only something that people normally grow is Kil'ayim.

(R. Chanina): R. Elazar forbids cactus because in Araviya people grow cactus for their camels.

Rejection: Araviya is a whole region. Menasiya is an individual. His opinion is Batel to that of normal people.

Answer: Rav Nachman holds like Rav Chisda;

(Rav Chisda): If one squeezed spinach and put the juice in a Mikveh, if it changes the appearance of the water, the Mikveh is Pasul.

Question: People do not normally squeeze spinach!

Answer #1: Since he considers it important, it is considered a liquid.

The same applies to squeezing pomegranates!

Rejection (and Answer #2 - Rav Papa): Spinach juice disqualifies a Mikveh because one may not make a Mikveh from it.

(Shmuel): One may squeeze grapes into a pot, but not into a bowl.

Inference (Rav Chisda): One may milk a goat into a pot, but not into a bowl.

He considers a liquid that goes into a solid like a solid.

145a (Rav): One may squeeze pickled vegetables for their sake, but not for the liquid. B'Di'eved, he is exempt.

One may squeeze cooked vegetables even for the liquid.

(Shmuel): One may squeeze pickled or cooked vegetables for their sake, but not for the liquid. B'Di'eved, he is exempt.

(R. Yochanan): Whether they are pickled or cooked, one may squeeze for their sake, but not for the liquid. B'Di'eved, he is Chayav Chatas.

Question (Beraisa): One may squeeze pickled vegetables needed for Shabbos, but not for Motza'ei Shabbos;

One may not squeeze olives and grapes. B'Di'eved, he is Chayav Chatas.

Answer (for R. Yochanan): It permits squeezing pickled vegetables needed for Shabbos, but not for Motza'ei Shabbos. The same applies to cooked vegetables;

This is for their sake, but not for the liquid. B'Di'eved, it is as if he squeezed olives and grapes. He is Chayav Chatas.

Rishonim

Rif (60b, citing R. Chananel): The Halachah does not follow Shmuel and Rav Chisda, rather, R. Yochanan. One may squeeze pickled or cooked vegetables for their sake, but not for the liquid. B'Di'eved, it is like squeezing olives and grapes, and he is Chayav Chatas. He did not distinguish squeezing into a bowl or pot. In both cases it is forbidden, just like olives and grapes. This shows that the Halachah does not follow Shmuel, and not Rav, who permits only into a pot.

Rebuttal (Rif): R. Yochanan is not Mechayev even into a pot. R. Yochanan taught that one who squeezes for their water is liable! R. Yochanan argues with Rav and Shmuel only about Isur and liability, but not about distinguishing a pot from a bowl. All agree that a liquid that goes into a food is like a food.

Rambam (Hilchos Shabbos 21:12): One may not squeeze berries and pomegranates. Since some people squeeze them like olives and grapes, perhaps one will come to squeeze olives and grapes. One may squeeze other Peros, such as quinces, apples and crabapples, for squeezing does not apply to them.

Rosh (22:2): All permit squeezing l'Chatchilah on Shabbos other Peros, e.g. plums, quinces, crabapples and similar fruits.

Poskim

Shulchan Aruch (OC 320:1): One may not squeeze berries and pomegranates. If the juice came out by itself, it is permitted if they were destined to be eaten, but forbidden if they were destined [to be squeezed] for liquid.

Gra (DH v'Tutim): The Rif and other Poskim rule like R. Yochanan. Perhaps R. Yochanan said so because he forbids an egg laid on Yom Tov due to a decree about juice that came from Peros. This forced him to switch the opinions in our Mishnah. (He rules like R. Yehudah, for he holds that this is really Chachamim's opinion.) We forbid the egg due to Hachanah. We need not switch the opinions. Presumably, we rule like Chachamim!

Mishnah Berurah (6): If one gathered them Stam, it is as if they are destined for liquid.

Shulchan Aruch (ibid.): One may squeeze all other fruits.

Beis Yosef (DH Tutim): Rashi explains that squeezing Peros is Mefarek, a Toladah of Dash. For Peros not normally squeezed, such as plums, Dash does not apply. R. Yerucham says that Rashi forbids squeezing any fruit. What many consider important is important, even if they are not the majority of the world, like Araviya. I equate everything squeezed for its juice to berries and pomegranates.

Magen Avraham (1): The Beis Yosef says that if we know that they squeeze a fruit in a certain place, one may not squeeze it, like pomegranates. This implies that it is forbidden everywhere. The Rema connotes that it is forbidden only there! He is correct. The Gemara asked according to R. Eliezer [regarding Kil'ayim]. We hold like Chachamim (YD 296:14), who forbid only where they grow it. Likewise, here we forbid only where they squeeze. If someone from Hutzal was Motzi on his head, he is exempt, even though in his city they do so (92a). Tosfos (92b DH v'Im) says that this is unlike Araviya. If everyone had camels like they do, also they would grow thorns! If everyone had pomegranates like Beis Menasiya, also they would squeeze them! Therefore, if a land conducts that way, it would be significant. However, only Menasiya did so. Rav Chisda's law is only when some people squeeze it. If it were not, there would be no need for the Beraisa to mention Beis Menasiya! Rather, others must do so. It need not be an entire city. It must be that others would do so if they had many such Peros. If not, Batlah Daito Etzel Kol Adam. The Bach and Semak permit other Peros only for the sake of the fruit, but not for the juice, and say that this is the custom. I say that where people squeeze in order to dip food into the juice, it is permitted, for it is not considered a liquid.

Kaf ha'Chayim (8): The Shulchan Aruch's opinion is primary. One may squeeze them even for the juice. L'Chatchilah, one should be concerned for the Bach.

Gra (DH v'She'ar): Rashi and Tosfos permit only for the sake of the fruit. This is in the first answer. According to Rav Papa [even for the fruit is permitted]. Why did Rav Nachman need to rule like the Tana? We must say that the first Tana argues, and holds that everywhere people squeeze pomegranates. The latter Tana forbids only due to Beis Menasiya. Rav Nachman rules like the latter Tana. This is relevant to other Peros, if they squeeze them in some place. We conclude unlike Rav Nachman. It is forbidden only in that place. The Rashba says that considering it important helps only if some squeeze them. If not, Batlah Daito Etzel Kol Adam. He says that R. Yonah, the Ramban, Rif, Rambam and other Poskim agree.

Rema: Where the custom is to squeeze a certain kind of fruit to drink the juice for thirst or pleasure, it is like berries and pomegranates. Only to squeeze is forbidden.

Gra (DH uv'Makom): All agree that where it is the custom [to squeeze], it is forbidden there, like we say about Kil'ayim (YD 296:14).

Mishnah Berurah (9): Even though in some places they squeeze apples, one may squeeze a cooked apple, for all of it comes out. (This is totally unlike Dash.)

Kaf ha'Chayim (9): The Rema forbids only where they squeeze it. However, he learns from the Beis Yosef, who forbids everywhere. Presumably, also the Rema forbids everywhere, even though his wording is awkward. He equates this to berries and pomegranates, which are forbidden everywhere.

Ashrei ha'Ish (2:28:1,3 citing ha'Gaon R. Y.S. Elyashiv Ztz"l):One should be stringent about citrus fruits destined to be squeezed for liquid. Perhaps most are planted for this. We are stringent to consider them like olives and grapes. Liquid that flows from them is forbidden, like what flows from olives and grapes. One may not cut them on a plate, for juice comes out. Even though this is a Pesik Reishei d'Lo Nicha Lei, it is not clear that we rule like the opinion that permits this when there is another reason why it is mid'Rabanan. (This is not the normal way to squeeze.) One may cut on a table, for then it is not considered squeezing, for the liquid is wasted.

Migdal David (Dash 73, at the end of Sefer "Lamed Tes Melachos", p.262): These laws depend on the current custom. Nowadays that almost no one squeezes pomegranates, and those who do, mix it with other liquids, they should be like other Peros that one may squeeze. Heaven forbid to be lenient in practice, for the Poskim forbade.