Zevachim, Chapter 7, Mishnah 3. This mishnah is quite simple, but it is based on two halachic concepts that are worth explaining beforehand: the tumah transmitted by the carcass of a kosher bird - the body of a kosher bird that was not slaughtered properly - and the law of me'ilah. Let us begin with the first concept.
The principles of neveilah tumah:
In terms of the laws of tumah and taharah, an animal carcass may or may not transmit tumah, and everything depends on the basic law of neveilah. The law of neveilah is generally limited to land mammals that are elevated off the ground (and regarding aquatic animals the matter is unclear). Among those animals, their carcasses transmit tumah: a dead cow, camel, goat, or horse - all of these transmit tumah, unless it is a kosher species that was properly slaughtered through shechitah. If a person properly slaughtered a goat, cow, sheep, giraffe, or deer - the carcass does not transmit tumah.
We can say, therefore, that every animal is like a neveilah - a potential source of tumah waiting to happen - and it can be saved from the status of neveilah by slaughtering it before it dies from other causes. This applies to regular land mammals, which are elevated above the ground.
In contrast, other animals do not transmit tumah at all:
A dead fly or a dead snake do not transmit tumah at all, even though they died.
The eight sheratzim - eight small, creeping, gnawing, and crawling creatures - their flesh transmits tumah through direct contact, but these are only eight specific species, and they are essentially the exception to the rule.
Fish do not transmit tumah when they die.
The tumah of a bird - two categories:
A non-kosher bird - such as an eagle, does not transmit tumah at all, just like a dead fish or a dead snake.
A kosher bird species - such as a chicken or a dove, can become a neveilah unless it is properly slaughtered. If it was properly slaughtered - it does not have the status of a neveilah and there is no tumah. If it was not properly slaughtered - it contains potential tumah, but its method of transmitting tumah is completely unique: tumah of the esophagus, meaning that at the moment it is swallowed, it transmits tumah to the one who swallows it.
Thus, one who touches the carcass of a chicken that died and was not properly slaughtered remains completely tahor, just like one who touches a dead snake, a dead fish, or a dead eagle. However, unlike the others, someone who actually swallows the flesh of that chicken - as the meat goes down his throat, beyond the cavity visible when opening the mouth - contracts tumah, and in a severe manner: as the meat goes down, the one swallowing it becomes an av hatumah, to the point that even his clothing becomes tamei.
The question of the mishnah:
The mishnah seeks to clarify the law regarding young pigeons and turtledoves, the two types of kosher birds offered in the Beis Hamikdash as a bird olah and a bird chatas: do they transmit tumah like a neveilah? If melikah was properly performed on them, it is obvious that there is no neveilah here, and the question is what the law is when they become invalidated.
For with a regular bird, like a chicken, the way to make it kosher is through shechitah with a knife at the front of the neck. If one performs melikah on a chicken, piercing the back of the neck with a thumbnail, it is a neveilah, and it transmits tumah in the esophagus at the time of swallowing. And here is the question: a kosher bird, such as a turtledove, that had melikah performed on it - which in the Beis Hamikdash is the proper way to prepare it - but the korban itself became invalidated; do we revert to viewing it as a neveilah that transmits tumah through swallowing, or not?
"Vechulan ein metamin b'veis habliah" - and all of them do not impart tumah in the esophagus:
The Mishnah states that all the cases listed until now - all the invalid cases where melikah was performed on a bird consecrated for a chatas or an olah and something went wrong in its service - are not neveilah. This includes:
He severed the head when he was not supposed to sever it.
He severed one siman and not both simanim.
He did not sprinkle the blood in the place where he was supposed to sprinkle it.
An improper thought, and anything similar.
All these do not change the halachah, and there is no neveilah here, because the bird was slaughtered in the way it is supposed to be slaughtered - with melikah in the Beis Hamikdash. Therefore, a person who ate from it, forgetting that the korban is invalid - the issue of the prohibition of eating is a different point, and there can be other consequences to that - but he does not become tamei through swallowing it. This is what the Mishnah means: "vechulan ein metamin b'veis habliah" - and all of them do not impart tumah in the esophagus. We will return to this matter later, but this is the basic idea.
"Umoalin bahen" - and they are subject to meilah:
The second thing the Mishnah says is that the law of meilah applies to them. Once a person has consecrated something, if it is in the category of kodshei Hashem - meaning the property of the Almighty - the law of meilah applies to it. This is the case with kodshei kodashim: the olah, chatas, and asham among animal sacrifices, as well as both types of birds - the olah of a bird and the chatas of a bird - both of which are kodshei kodashim. As long as no one can eat them in their current status, they are subject to meilah, and anyone who derives a perutah's worth of benefit from this bird, whether alive or dead, is subject to the laws of meilah.
When the chatas of a bird is offered properly, after the sprinkling of the blood on the altar, it ceases to be kodshei kodashim and stops being subject to meilah, because from now on it becomes food for the kohanim - the food of kohanim and not the property of the Almighty, so to speak, and therefore there is no longer any meilah in it.
Hence the question: a chatas of a bird or an olah of a bird that was performed improperly, and is not designated to be eaten by the kohanim - does the law of meilah remain in it as at first, as kodashim, even after it became invalid? The answer is that indeed it does, and therefore the Mishnah says "umoalin bahen" - they are subject to meilah, but with one exception.
"Chutz mechatas ha'of she'asah lematah kema'aseh chatas leshem chatas" - except for the chatas of a bird that he performed below like the procedure of a chatas, for the sake of a chatas:
This is the very first case in our chapter, where the chatas of a bird was performed according to the law - in the right place, in the right way, and with the right intentions - and it is a valid chatas. And since it is a valid chatas, its status changed from kodshei Hashem, which are subject to meilah, to the food of a kohen, and meilah no longer applies to it.
In summary: In this Mishnah we learned two halachos regarding birds that became invalid. The first: "vechulan ein metamin b'veis habliah" - all the invalid cases listed in the chapter, where melikah was performed on them in the manner of their validation in the Beis Hamikdash, are not neveilah, and even though eating them is forbidden, one who swallows them does not become tamei. The second: "umoalin bahen" - their status as kodshei Hashem is not revoked by their invalidation, and therefore the law of meilah remains upon them, except for the chatas of a bird that was performed according to its law below, like the procedure of a chatas, for the sake of a chatas, which, since it was validated and became the food of kohanim, is not subject to meilah.