Taharos, Chapter 1, Mishnah 3. The opening mishnayos of this chapter map out the tumah of a bird that died without shechitah. Until now the discussion centered on the neveilah of an of tahor, a bird from a kosher species, whose carcass carries its own unusual set of rules. Our mishnah turns to the reverse case: the neveilah of an of tamei, a bird of a species that could never be eaten in the first place. Picture a vulture or something similar. Even had it received a flawless shechitah it would still be forbidden, and here it happens to have died on its own. The Mishnah lists, point by point, how this carcass differs from the carcass of, say, a chicken.
The starting point is a pasuk in Vayikra, chapter 22, which addresses the kohanim: "Neveilah u'treifah lo yochal l'tam'ah vah, ani Hashem" - he shall not eat a neveilah or a treifah, to become tamei through it. Notice the verb. In the case of the kosher bird, the Torah's operative word was yochal, eating, and consequently all the striking features of that neveilah flowed from its status as an item of food. Here the word is lo yochal, it may not be eaten. This bird is simply not on the menu, and therefore none of the eating-driven consequences carry over. With that in hand, we can work through the list.
"Nivlas of hatamei tzrichah machshavah v'hechsher" - the carcass of a non-kosher bird requires both intent and preparation. Machshavah means that someone must actually designate it as food. Since nobody would assume on his own that such a carcass is meant to be eaten, the entire framework of food tumah only engages once a person has that intention. Hechsher means that it must be wetted and then come into contact with a source of tumah, such as a sheretz, in order to be able to receive impurity at all.
"U'metamei tumas ochlin k'beitzah" - it conveys the tumah of foods in the volume of an egg. In the case of the kosher bird's neveilah the measure was a k'zayis, precisely because there the halachah was engaging the carcass as something being eaten. Here, where eating is not in play, we revert to the standard measure of a food item, a k'beitzah.
"V'k'chatzi pras lifsol es haguf" - half of a pras is needed to disqualify the body of the person who eats it. A pras is a loaf of bread, and its exact size is the subject of a four-way machlokes among the Tannaim, measured in relation to a k'beitzah. The Rishonim then argue over which of those Tannaim we follow in practice. That debate is not our concern here; what matters for our mishnah is that the measure for rendering the body itself unfit is half a pras.
"V'ein bah k'zayis b'veis habeli'ah" - there is no rule here of a k'zayis in the throat. With the kosher bird's neveilah, swallowing a k'zayis triggered tumah; with this carcass, it does not.
"V'ha'ochlah eino tzarich he'erev shemesh" - one who eats it does not need to wait for nightfall. Immersion in a mikveh is sufficient; he need not wait out the day until the sun sets.
"V'ein chayavin aleha al bi'as Mikdash" - and one is not liable for entering the Mikdash in this state. The Bartenura explains the reason: when all is said and done, this tumah is only rabbinic in origin, a tumah d'rabbanan, and rabbinic tumah does not generate liability for entering the Mikdash.
"Aval sorfin aleha es haterumah" - nevertheless, terumah that came into contact with it is burned. Even though we are dealing with a rabbinic level of tumah, we are still prepared to destroy terumah on its account, a consequence whose weight will come up again later in the masechta.
"V'ha'ochel eiver min hachai mimenah eino sofeg es ha'arba'im" - one who eats a limb torn from this creature while it was alive does not receive the forty lashes. The prohibition of eiver min hachai attaches only to a species that is otherwise fit for eating. Since a non-kosher bird is forbidden to begin with, there is no separate violation of eiver min hachai to punish.
"V'ein shechitasah metaharatah" - and shechitah does not purify it. In the case of the kosher bird's neveilah, shechitah provided a way out of the tumah; here it accomplishes nothing. The Bartenura raises the obvious question: who exactly is performing shechitah on a non-kosher bird? The statement cannot be taken at face value, and the Gemara in Chullin supplies a scenario. A Jew is slaughtering the animal for a ben Noach. Now, something noteworthy happens in the shechitah process: an animal often dies at once, yet its body continues to twitch and convulse afterward. While it is in that state, a Jew may eat it, but a non-Jew, who is bound by the prohibition of a limb from a living animal, must wait until death is complete. The logic runs that we cannot hold the non-Jew to a stricter standard than the Jew: if a Jew may eat the animal while it is still convulsing, so may the non-Jew. In our case, however, that logic collapses, because this is a species the Jew may not eat at all. The non-Jew therefore has to wait until the animal has fully died.
"Haknafayim v'hanotzah mitam'os u'mitztarfos" - the wings and the feathers receive tumah and combine toward the measure. They serve as a shomer, a protective covering for the flesh, and so they are counted along with it. "V'hachartom v'hatziparnayim mitam'in u'mitztarfin" - the beak and the claws likewise receive tumah and combine, exactly as we find with the kosher bird. The Mishnah states it here for the sake of the parallel between the two cases.
What emerges from the whole list is a single theme. The carcass of a non-kosher bird is never a candidate for eating, so every halachah that depended on eating drops away, and what remains is the ordinary framework of a food item that a person chose to treat as food.