Gemara

48a (Rav Yehudah): If one opens the neck-opening of a garment, he is Chayav Chatas.

74b (Mishnah): Tearing in order to sew [is an Av Melachah].

(Rabah and R. Zeira): If worms made a hole in a curtain, they would tear it and sew it up.

105b (Mishnah): If one tore out of anger or due to his Mes, or did anything destructive, he is exempt;

If one ruined something in order to fix it, the Shi'ur to be liable is like one who fixes.

Contradiction (Beraisa): If one tore out of anger, or if a mourner tore [his clothing] due to his Mes, he is liable for Chilul Shabbos. Even so, he fulfilled his obligation to tear.

Answer: The Beraisa is R. Yehudah, who is Mechayev for Melachah she'Einah Tzerichah l'Gufah. The Mishnah is R. Shimon, who exempts.

Question: Is R. Yehudah Mechayev for something destructive?!

Answer #1 (R. Avin): It is considered constructive, for it calms his anger.

Answer #2: He did so to instill fear in his household;

106a (Mishnah): If one did anything destructive, he is exempt.

Rishonim

Rambam (Hilchos Shabbos 10:10): If one tears in order to sew two stitches, he is liable. If one tore to ruin he is exempt, for he is Mekalkel. If one tore out of anger or due to his Mes over which he must mourn, he is liable, for this calms his mind and Yetzer. Therefore, this is like Tikun. One who opens the neck hole of a shirt is liable.

Kesef Mishneh: The Ritva (Makos 3b DH Amar) says that Rashi explains that we discuss one who opened an opening for the neck for the first time. He is liable for Tikun Maneh. He is not liable for Kore'a, for it is not in order to sew. The Ritva challenged this, and brought R. Tam, who says that it was previously opened, but sewn shut.

Rambam (11): If one separates papers or hides stuck together, without intent for pure Kilkul, he is liable for a Toladah of Kore'a (tearing).

Rambam (22:4): If one's garment became tangled in thorns, he removes it covertly and gently, lest it tear. If it tore, it tore. (There is no problem.) Similarly, one may wear new garments. If it tore, it tore, for he does not intend to tear. One may bang on a cloth to crack nuts underneath, without concern lest it tear.

Tosfos (73b DH v'Tzarich): Even R. Yehudah, who obligates for Melachah she'Einah Tzerichah l'Gufah, obligates for reaping only if he needs the wood [that he detaches]. This is like tearing in order to sew, and erasing in order to write. R. Yochanan taught that one may squeeze pickled or cooked vegetables for the vegetables. If one squeezes them for the liquid inside, he is liable. Why do we permit for the vegetables? This should be like Melachah she'Einah Tzerichah l'Gufah! Rather, it is because this is not the way of Dishah (threshing).

Poskim

Shulchan Aruch (OC 317:3): One may not open the neck-hole in a new garment, for this is Tikun Maneh.

Beis Yosef (DH Matirin): Rashi obligates for Makeh b'Patish, for now he makes it a Kli. Why isn't he liable for Kore'a? I answer that one is liable for Kore'a only if it is in order to sew (73a). Here, it is not in order to sew.

Magen Avraham (10): See also Kesef Mishneh 10:10. This is unlike Olas Shabbos.

Machatzis ha'Shekel: Olas Shabbos asked that Kore'a must be in order to sew only so it will not be Mekalkel. (He proves this from the Rambam, who obligates for tearing out of anger - Eshel Avraham.) Here it is not Mekalkel, so he should be liable for Kore'a! I do not see how the Kesef Mishneh answers this.

Nishmas Adam (29:1): Why did the Beis Yosef omit the Rambam's opinion, that one is liable for Kore'a? It is because he favors the opinion that exempts Melachah she'Einah Tzerichah l'Gufah. However, why did he write Stam like the Rambam in Siman 340? This requires investigation.

Shulchan Aruch (340:14): If one separates papers or hides stuck together, not with intent for pure Kilkul, he is liable for a Toladah of Kore'a.

Mishnah Berurah (43): If he intended for any benefit, even without intent to stick them together again, he is liable. We do not require Kore'a with intent to sew. Intent for any Tikun suffices so that it is not considered Mekalkel. If he intends for Kilkul he is exempt, like all Mekalkelim.

Mishnah Berurah (44): All the more so, one who tears on a seam in a garment, for some benefit, is liable.

Mishnah Berurah (45): If papers were stuck together in the place of the letters, one may not separate them [due to erasing]. If pages of a Sefer were not cut before Shabbos, one who separates them is liable. One may not do so even through a Nochri.

R. Akiva Eiger (73a DH ha'Kore'a): The Gemara connotes that if Kore'a is not in order to sew, it is exempt because it is Mekalkel. However, we find that one is liable for tearing out of anger or due to a Mes. However, the Beis Yosef exempted for Kore'a, since it is not in order to sew. The Magen Avraham agreed. Olas Shabbos asked my question. Also Tosfos (73b) says like the Beis Yosef. He says just like Kore'a is only in order to sew, reaping without need for the wood is not reaping. This requires great investigation.

Bi'ur Halachah (DH v'Lo): The Rambam taught opening the neck opening to teach that Kore'a is liable for any Tikun, even if it is not in order to sew. The Beis Yosef said that one is liable for Kore'a only if it is in order to sew. Here, he wrote in the Shulchan Aruch like the Rambam, that one is liable for any Tikun! R. Akiva Eiger brought a clear proof from tearing out of anger or due to a Mes (i.e. for close relatives. One may not sew it back later.) Also Nishmas Adam says like I said. I can defend Tosfos. Tosfos did not literally mean that one is liable for Kore'a only with intent to sew. He merely adopted the usual expression (Kore'a in order to sew) to show that without Tikun, it is not called Kore'a, for it is Mekalkel, and similarly reaping without need for the wood is not reaping.

Note: I do not understand his answer. If one is liable for Kore'a without Tikun in the matter torn, how can we learn that reaping is liable only if there is Tikun in the matter detached? The Oz v'Hadar Mishnah Berurah explains that the Bi'ur Halachah means 'just like Kore'a must have a Tikun in the garment...' I do not understand this. Tearing out of anger is not a Tikun in the garment!

Bi'ur Halachah: A support for my answer is Tosfos (94a DH R. Shimon. He says that Kore'a in the Mishkan was in order to fix something torn.) He did not say that it was in order to sew it!

Question (Nishmas Adam 29:1) Tearing papers, or any Kore'a for Tikun is liable only if Melachah she'Einah Tzerichah l'Gufah is liable. If not, one is liable only for Kore'a in order to sew. Why did the Shulchan Aruch bring the Rambam's law Stam? Above, in 316:8 and 334:27, the Shulchan Aruch favors the opinion that Melachah she'Einah Tzerichah l'Gufah is exempt!

Answer (Bi'ur Halachah): Tosfos (105b DH Ha) holds that tearing over one's Mes (i.e. over a relative over whom he must mourn) is Tikun Mitzvah. It is called Melachah ha'Tzerichah l'Gufah. The same applies to every Kore'a of Tikun. Rashi (105b DH Ha) holds that tearing over one's Mes is exempt, due to Melachah she'Einah Tzerichah l'Gufah. I.e. he holds that Tikun Mitzvah is not a big enough Tikun to make the Melachah considered Tzerichah l'Gufah. However, any needed Tikun, e.g. to separate papers so they will be thin, all agree that it is Melachah ha'Tzerichah l'Gufah, just like tearing in order to sew. We exempt tearing out of anger according to the opinion that exempts Melachah she'Einah Tzerichah l'Gufah, because there is no Tikun in the garment. Rashi exempts tearing due to a Mes because it is Melachah she'Einah Tzerichah l'Gufah, just like Hotza'ah of a Mes to bury it [93b DH R. Shimon, for he would have preferred if the entire matter never happened]. He did not simply exempt because it is without intent to sew! Rather, even Rashi obligates when he wants the Tikun of the tearing. Also the Ba'al ha'Ma'or (38a) connotes like this. He says that R. Shimon exempts one who tears to instill fear, because he does not need the Melachah itself. Had he needed the tearing, even though it is not in order to sew, he would be liable. R. Yerucham rules like R. Shimon, but he obligates one who tears due to a Mes. Also the Me'iri (105b DH Kore'a) says that intent for Tikun, even not to sew, suffices.

Bi'ur Halachah: The Rambam, Rashi and Tosfos do not require in order to sew, even according to R. Shimon, just Tosfos requires Tikun in the matter torn. The Kesef Mishneh brought the Ritva who obligates Kore'a only if it is in order to sew. This is a lone opinion. The Sugya on 105b opposes him. The Beis Yosef retracted here to say so. The Pri Chodosh said so. Nishmas Adam improperly challenged him. Why does Rashi (48a DH Chayav) obligate for opening the neck hole due to Makeh b'Patish, and not due to Kore'a in order to fix? I say that he holds that Kore'a is only when he is Mekalkel at the time, but he intends for a Tikun, like tearing worm-eaten curtains in the Mishkan.

Igros Moshe (OC 1:122, Anaf 10): Letter of the law, one may open cans and packages that most people normally throw out after the contents are removed, especially since most are ruined through opening them. However, since there are few Bnei Torah, one should be stringent, lest people come to be [more] lenient. The greatest honor to Shabbos and Yom Tov is to refrain from opening them. If there is a great need, e.g. he invited guests and he would be ashamed [if he lacks food for them], he should break them through a Nochri. If there is no Nochri, a Chacham may break them covertly. Regarding Yom Tov, if he could not have opened it before Yom Tov, he may break it. If the contents would spoil had he opened it before Yom Tov, this is permitted l'Chatchilah to all.