Gemara

(Mishnah): If an Achbar is half flesh... (one who touches the flesh becomes Tamei).

R. Yehudah says, even one who touches the earth opposite the flesh is Tamei.

Sanhedrin 91a - Question (a Min): You say that the dead will live. They are earth! Earth does not live!

R. Ami: If you do not believe me (that Hash-m can make life from earth) go look at a mouse that is currently half-earth. Later, it will be a full mouse!

Shabbos 12a (Beraisa - R. Eliezer): If one kills a Kinah (louse) on Shabbos he is (liable) like one who killed a camel.

Rav Nachman (to his daughters): Kill Ma'acholos (lice), so I will hear the death of my enemies!

(Beraisa - R. Shimon ben Elazar): Beis Hillel permit killing lice on Shabbos.

107b (Rav Yosef): Chachamim (of R. Eliezer) exempt one who kills a louse on Shabbos, for they do not reproduce (sexually).

Both of them learn from rams;

R. Eliezer says, just like they were killed (for their skins, for the Mishkan), one is liable for killing anything;

Chachamim say, just like they reproduce, one is liable for anything that reproduces.

Question: A Pir'osh (flea or louse) reproduces, yet R. Yehoshua exempts!

(Beraisa - R. Eliezer): If one traps a Pir'osh on Shabbos, he is liable;

R. Yehoshua exempts.

Answer (Rav Ashi): Trapping is unlike killing!

R. Eliezer obligates even if the species is not normally hunted, and R. Yehoshua exempts in such a case. However, R. Yehoshua agrees that he is liable for killing them!

Rishonim

Rambam (Hilchos Shabbos 11:2): If vermin reproduce from male and female, or develop from earth, like Pir'oshim, one who kills them is liable like one who kills an animal. If vermin develop from excrement or rotting Peros or similar things, e.g. worms of meat or in legumes, one who kills them is exempt.

Magen Avraham (316:20): The Magid Mishneh connotes that when the Rambam says 'exempt', he means permitted, like a Kinah. However, one may not kill worms that grow in attached Peros, for they are proper Sheratzim.

Lechem Mishneh: The Rambam forbids killing worms that develop in meat or legumes. He permits (Halachah 3) killing lice that develop from sweat.

Rambam (3): One may kill lice on Shabbos, for they are from sweat.

Perush ha'Mishnayos (Chulin 9:6): The mouse that develops from earth is famous. One cannot count the number of people who told me that they saw it. The existence of such a creature is a wonder that we cannot explain at all.

Sefer ha'Mitzvos (Lav 179): Do not think that a bird cannot develop from rotting Peros. We see that this occurs. The birds are bigger than a small nut. The Gemara says that one is lashed five times for eating a Nemalah (the Rambam understands that it is not an ant). This Nemalah jumps, and it develops from rotting Peros. It does not reproduce. Also the Tzir'ah (for which one is lashed six times) develops from rotting Peros. Fools think that all reproduction must be from male and female, since most species are like this.

R. Avraham ben ha'Rambam (brought in introduction to Ein Yakov, DH Da Ki Atah): In spite of the greatness of Chachamim and their expertise in explaining all laws of the Torah, we do not rely on everything they said about medicine, science and astonomy. We find that some of their Refu'os do not work, e.g. the stone to prevent miscarriage, and what they said in Shabbos Perek 14 (perhaps he alludes to what it says about Pir'osh - PF.)

Moreh Nevuchim (1:72): Several kinds of worms develop from wasteheaps. Anything unable to reproduce itself is in this category.

Rashi (67b DH Minah): Worms found in the liver or lungs grow from the animals themselves.

Tosfos (67b DH Lerabos): Worms in animals are created from the meat itself.

Rashi (126b DH Yesh): The mouse does not reproduce. It develops by itself from earth, just like a wasteheap breeds worms.

Boaz (Chulin 9:2): Some Apikorsim mock the mouse that develops from earth mentioned in the Mishnah. There was a famous scientist Link, and in his book Orwalt (1 p.327) he says that he saw it in Mitzrayim. It is called springmouse. The head, chest and forelegs are delineated well, but the back is still formless dirt. After some days, it is all flesh. He said 'how great are your works Hash-m!'

Sichas Chulin (p.533): Link referred to the species called Yarbo'a (Rashi Sanhedrin 91a - squirrel). Scientists say that they cannot see it reproduce, for it gives birth in tunnels in the ground. Some say that they saw it give birth in captivity; the Gemara discusses it in its natural state.

Ran (Shabbos 5a DH Amar): Some say that Kinah is the black flea that jumps, and Pir'osh is the one that crawls. R. Tam says oppositely. Why do we forbid the flea? It develops from earth, and does not reproduce! We can say that we require reproduction to exclude vermin that come from what rots, like Kinim, but what comes from earth has life, as if it reproduced from a male and female. The Rambam says so. Shabbos 107b means that the law of a Pir'osh is as if it reproduced. However, the Ramban says that the Pir'osh of the Gemara is another species that reproduces.

Ran (DH u'Veis): Lice do not reproduce. They breed from man's skin.

Ritva (12a DH ha'Horeg): Rashi says that the Kinah and Ma'acholes discussed here develop from sweat on the head, i.e. Pudul. Also R. Tam says that it is common on the head. The Medrash (Koheles 5:13) supports this. In Nidah (20b) we say that a comb is used to kill Kinim in the head. We know that it kills Pudul. Even though in Mitzrayim the Kinim came from earth, and normally only Putza develops from earth, and Nidah 52 calls Ma'acholes what we call Putza, we must say that Beis Hillel do not permit Putza, for it reproduces. Rather, they permit only Pudul that develops from sweat. Tana'im argue about trapping Putza, but all agree that one may not kill it (on Shabbos). The Ge'onim said that Chachamim did not obligate for killing all Pir'oshim, rather, only Bragis, for they reproduce. Those that develop from earth are like Kinim. Perhaps they are in the category of Makas Kinim. The same applies to Ma'acholos discussed regarding stains. It is proper to be stringent

Poskim

Shulchan Aruch (OC 316:9): On Shabbos, one may not kill a Pir'osh.

Mishbetzos Zahav (6): Tosfos says that a Pir'osh reproduces. We must say that some develop from earth, and some reproduce, like mice (some develop from earth, and some reproduce). The Mechaber did not say that one is liable for killing it. He is unsure. Perhaps it does not reproduce, and Pir'osh is a different species.

Kaf ha'Chayim (76): One is liable only if he killed it in a way that was Tzerichah l'Gufah, but not if it was just so it will not bite him.

R. E.M. Horowitz (12a DH Rava) Rav Nachman said 'kill them, so I will hear the death of my enemies' in order to publicize that the Halachah follows Beis Hillel, who totally permit killing lice, even in a vengeful way, i.e. Tzerichah l'Gufah.

Mishnah Berurah (36): This is unlike some Poskim, who hold that it is like a Kinah, and one may trap and kill it. If it is a Safek whether it is a Pir'osh or Kinah, e.g. at night, one may trap it, but not kill it. One may delouse clothing from Pir'oshim, without taking them by hand, for this is trapping. He merely makes them fall down.

Mishnah Berurah (38): Even if a Pir'osh is biting him, he may not kill it.

Rema: One may kill a Kinah.

Beis Yosef (DH veha'Rav): The Rambam holds like R. Tam, that a Pir'osh develops from earth; one who kills it is liable. A Kinah develops from sweat; one may kill it. The black flea that jumps develops from earth; white lice come from sweat. Since the Rambam and Rosh agree with R. Tam, we hold like him.

Mishnah Berurah (41): One is exempt for worms in detached Peros only if they developed after they rotted.

Michtav me'Eliyahu (Vol. 4, p.355, footnote 4, in the name of the author): Accepted Halachos are not changed by scientific discoveries, e.g. one may kill lice even though we find that they do reproduce through male and female. Chachamim transmitted known Halachos that are not dependent on the explanations given. Sometimes, Chachamim gave explanations based on the current scientific knowledge.

Hagahah (R. Aryeh Karmel): The Halachah depends only on what can be sensed. Perhaps lice eggs were too small to be seen at the time of Matan Torah. Therefore, lice are considered to develop from the substance in which they grow and are fed from. Perhaps we can say the same about Sheratzim that grow in Peros. Since we do not see the eggs, they are considered to grow from the Pri itself.

Menuchas Ahavah (3:18:6): Since they cannot hatch without sweat, this is not considered reproduction from male and female (alone. In the appendix, he cites the Rambam and others who say that Chazal's words on matters like this were not all based on prophecy, tradition or Ru'ach ha'Kodesh. The Yerushalmi says that one may kill lice because they have meager life (anything without a spine cannot live more than six months), but the Bavli argues with this; it obligates for killing a Pir'osh).

Yalkut Yosef (316, p.547): Pachas Yitzchak (Tzeidah 21b) and others some others say that nowadays that we see that head lice reproduce and lay eggs, one may not kill them on Shabbos. His son said that we do not deviate from what Chazal said, even to be stringent. Michtav me'Eliyahu said similarly.