Having warned against eating all the Tamei species, why does the Torah see fit to add "Lehavdil ... bein ha'Tahor u'veun ha'Tamei"?
Rashi: To teach us that it is not sufficient to learn about the distinction between the Tahor and Tamei species, one also needs to be proficient in being able to discern the difference between them.
Hadar Zekenim and Ba'al ha'Turim: The Pasuk begins and ends with the letter 'Lamed'. Together, their Gematriya is sixty - to teach us that Isur is Batel in sixty parts of Heter. 1
Surely this is a mere Asmachta, since Bitul in sixty is not a Gezeiras ha'Kasuv. Rather, the Chachamim gauged that almost all Isurim do not give taste to sixty times their own volume, (there are exceptions - refer to 11:11:151:3). That is why the Ba'al ha'Turim writes, not that we learn from there, but that it is a hint. One opinion in Chulin 98a-b learns it from the foreleg of Eil Nazir, which is forbidden to Zarim, yet it is cooked together with the ram (which is sixty times its size) and does not render it forbidden. (PF).
What is the Torah adding when it writes "Bein ha'Tamei u'Vein ha'Tahor"?
Rashi and Ramban #2: It is certainly not coming to instruct us to distinguish between a donkey and a cow, since their respective Simanim are clear-cut. It must therefore coming to distinguish between where the Shochet has Shechted half the Simanim and where he has Shechted the majority. 1
Ramban #1: The Torah is adding an obligation here to clarify the difference between the species that render a person Tamei and those that don't.
Shevu'os, 18b #1: Based on the juxtaposition of "Lehavdil bein ha'Tahor u'Vein ha'Tamei" to "Ishah ki Yaldah Zachar" (in 12:2), it teaches us that anyone who separates from his wife close to her period 2 will merit to have sons.
Shevu'os #2, 18b: See answer #3. The Torah uses the same same Lashon "Lehavdil bein ha'Tahor u'Vein ha'Tamei" earlier in 10:10, and it also writes writes there "Lehavdil bein ha'Kodesh u'vein ha'Chol", to teach us (by virtue of the same juxtaposition) that whoever makes Havdalah over wine too will merit to have sons. 3
What is the Torah adding when it concludes "u'Vein Chayah ha'Ne'echeles ... ", which seems obvious?
Rashi and Targum Yonasan: It is a warning to learn the distinction between a wound that renders an animal a T'reifah 1 and one that does not. 2
Ramban #1: With reference to "Nefesh" in the previous Pasuk, it is a Mitzvah to distinguish between the creatures that live in the water or on dry land that may be eaten, and those that may not be eaten.
Ramban #2 (citing the Sifra): This adds a La'av for Tamei Chayos.
Riva #1: To distinguish between a limb of a fetus that is stuck outside the womb, which the Shechitah does not permit since we apply "u'Basar ba'Sadeh Tereifah [Lo Socheilu]" ? and one which returned inside before the Shechitah, it is permitted. 3
Riva #2: To distinguish between the eighteen aberrations that render an animal a T'reifah 4 - such as an extra or missing hind leg, and those that do not - such as an extra or missing foreleg.
Sifsei Chachamim: With reference to the eighteen T'reifos. See also Ba'al ha'Turim/
Rashi: It cannot be a warning to distinguish between a deer and a wild ass, since their Simanim were already taught.
This is like R. Yochanan whose opinion is refuted (Chulin 68b) - in which case it is forbidden even if it returned! (PF)
See Torah Temimah, who elaborates.
The Pasuk mentions distinguishing "between the Tamei and Tahor, between Chayos that you may eat..." - why did it switch the order, and mention first the Heter?
RS"R Hirsh (20:25): Whenever the Torah obligates distinguishing, we must ensure that the two kinds do not mix. One may not be Metaher what is Tamei or Metamei what is Tahor, or to forbid what is permitted (Yerushalmi Terumos Sof Perek 5). 1
Also later - in 20:25, it switches the order in the same way.
