Gemara

(Beraisa): One may inspect (a Mum on) any Bechor, except for his own;

He may inspect (even) his own Kodshim (except for Bechor) or Ma'aser (Behemah), and rule about his own Taharos.

Question: In what case may one inspect any Bechor except for his own?

One person may not check by himself. Three are needed!

Answer #1: He is one of three that check.

Rejection: If so, he would not be suspected!

(Mishnah): If Leah did Mi'un or Chalitzah in front of Reuven, he may marry her, because this requires a Beis Din. (We do not suspect the other judges!)

Answer #2: Really, he checks by himself, like Rav Chisda taught (elsewhere) that an expert is like three (regarding permitting vows). Here also, one expert may check a Mum.

He is not suspected about his own Kodshim (other than Bechor), for he could retract his Hekdesh (like Hataras Nedarim) if he wanted;

He is not suspected about his own Ma'aser, for he could have blemished his entire herd before tithing. (They were Chulin at the time.)

He is not suspected about his own Taharos, for even if they are Teme'im, he could eat them when he is Tamei.

Eruvin 63a (Rava): A Chacham may inspect his own knife (even though it was enacted that a Shochet must bring his knife to the local Chacham to inspect it, for the honor of the Chacham).

Rishonim

Rambam (Hilchos Ma'achalos Asuros 8:7): If a butcher is Muchzak to be Kosher, he slaughters by himself and sells to others, and he is believed.

Rivash (500): If a butcher is Muchzak to be Kosher, he may slaughter by himself and sell to others. We are not concerned for suspicion.

Hagahos Ashri (Chulin 1:14, citing the Mordechai): Or Zaru'a asked why a Shochet is believed. One witness is not believed against Chezkas Isur. R. Eliezer mi'Mitz answered that a crude, lowly witness is not believed against Chezkas Isur, even though the Torah believes two such witnesses (about anything). One who is established to be Kosher, even a woman, is believed about Isurim. R. Tam holds that one is believed about what was once b'Yado (in his control). R. Baruch says that since most who slaughter are experts, we do not require two, even though there was Chezkas Isur.

R. Shimshon (Nega'im 2:5 DH she'Beinah): A Tosefta teaches that one may check his own Kodshim and Ma'aser Behemah, because he could permit his Hekdesh or blemish them. He may rule about his own Taharos, for even if they are Teme'im, he could eat them when he is Tamei. If so, why may he rule about his Terumah? If it is Tamei, it is worthless! It is difficult to say that he is not believed. In Eruvin (63a) we say that a Chacham may check (his knife) for himself. A Tosefta teaches that a Kohen is believed about his own Tzara'as. Perhaps this is only when there is no Chezkas Isur. Perhaps we rely on one witness for Isurim only in such cases (Yevamos 88a). A Chacham may check for himself only if no Isur was Muchzak.

Tosfos (31a DH d'Ha): One may rule about his own Taharos, for even if they are Teme'im, he could eat them when he is Tamei. If so, will we say that he may not rule about his Terumah, for if it is Tamei, it is worthless?! The same applies to all other Isur v'Heter.

Chavos Ya'ir (122): I add to Tosfos' question. Why is one not believed about his own Bechor? If we suspect lest he permit it through a temporary Mum, he could blemish it, even though this is forbidden. Chazal were not concerned lest one intentionally lie to permit something to himself, except for a great matter that a person lusts for and he has no other way to get it. I.e. when a woman is captured, her husband is not believed to say that she is Tahor. He is believed about another woman. If Reuven says 'I killed Ploni', he may not marry Ploni's widow. This is not because we suspect that Reuven is lying. It is only to avoid gossip. This is why if he married her, he need not divorce her. When two or three people permit something, Chachamim were not concerned lest people suspect lest they lied. (Therefore, one of them may benefit from it or marry her...) They decreed only about a matter that has publicity, such as permitting a Bechor. Taharos is similar, therefore we needed a reason (he could eat Tamei food when he is Tamei). Normal rulings that occur in one's house lack publicity. A Gezeras ha'Kasuv forbids ruling about one's own Tzara'as. R. Meir and Chachamim argue about whether we equate Tzara'as to monetary cases to disqualify relatives. Likewise, a verse teaches that one may not permit his own vows. R. Yehudah holds that one may not permit his wife's vows. This is not due to suspicion, for if so, he would join with two others. Rather, it is because one's wife is like oneself. A Hagahah in R. Shimshon says so, and also YD 234:57. What forced R. Shimshon to say that it depends on whether there is Chezkas Isur? There was no question at all. Surely one is believed about his own Tzara'as, e.g. to tell the Kohen that the white hair preceded the Tzara'as. A Gezeras ha'Kasuv obligates that another Kohen declare it Tamei or Tahor, even if the afflicted person is a Kohen, just like a Gezeras ha'Kasuv obligates a Kohen to rule about it. Surely the person himself is believed, even against a witness who testifies against him, like we say in YD 127:1 (regarding Yayin Nesech), from the Sugya in Yevamos (87b).

Poskim

Shulchan Aruch (YD 312:2): A Chacham may not inspect his own Bechor.

Taz (4): This is due to suspicion. However, the Rema (18:18) says that in some places, the custom is that a Shochet does not check for himself. This implies that letter of the law, it is permitted! R. Shimshon forbids when the Isur was Muchzak. This can answer my question. Once the animal was slaughtered, it is Muchzak to be Kosher, and there is no Chezkas Isur. Do not say that if so, one should not believed about his own regarding Shechitah, for the animal has Chezkas Isur while it is alive. For this, we rely on the fact that the majority of those who slaughter are experts, like the Mordechai says.

Question (Chavos Ya'ir 122): How does it help that most who slaughter are experts? Perhaps he paused or pressed! Tosfos (Nidah 20b DH Kol) says that a Chacham may see his wife's blood (to determine if it makes her a Nidah), since the Mishnah did not forbid this. Why did Rav Nachman's wife normally ask Rabah bar bar Chanah to check her blood? Tosfos answered that perhaps Rav Nachman was not an expert, or she was concerned lest he be stringent. R. Shimshon answered that she was concerned lest this make her lowly in his eyes. Tosfos did not answer that there was (Chezkas) Isur (so Rav Nachman is not believed to permit for himself). This shows that Hora'ah (a ruling) is not called Chezkas Isur. If so, the question would remain, that one may rule about his own only if in any case it is useful (even if he will forbid, e.g. Taharos) when he is Tamei.

Chavos Ya'ir: If we would permit Bechoros nowadays through one expert, surely he could not permit his own. Do not say that the concern was only for subtle differences between permanent and temporary Mumim, but nowadays that we require overt Mumim such as a blinded eye, there is no concern. This is wrong. The Sugya compares Bechoros to Mi'un, Chalitzah, Get and testimony about death. This shows that there is concern for overt lying. Also, even nowadays one must discern between holes in different parts of the ear, and a crevice in which a fingernail gets caught. However, since nowadays we permit only through three, one is believed about his own. Even when one used to permit, one was believed about his brother. Even when we are concerned for suspicion (and forbid one who permitted a woman to marry her), his son or brother may marry her (Yevamos 26a). Other matters one may permit for himself, even in the region of his Rebbi, like it says in Eruvin. One may not judge or testify about a matter that could benefit him, even if there is a very small chance of getting even a small Hana'ah.

Pischei Teshuvah (1): The Gemara said that we must discuss an expert who permits by himself, for if he is one of three, there is no suspicion. Tosfos Yom Tov says so, and Ma'adanei Melech says that this is why the Rosh omitted this (for nowadays one expert does not permit Bechoros). However, even nowadays this is relevant if all three judges own a share of the animal. Rashi said that three are not suspected to lie for the sake of one of them, but if all of them own a share, perhaps they are suspected. However, in several places it seems that there is no suspicion.

Shulchan Aruch (YD 18:18): A butcher must be paid equally for slaughtering Trefos as for Kosher animals.

Rema: This is lest he be lenient to permit in order to receive his wage. Therefore, in some places, the custom is that a Shochet does not check for himself, rather, appointees of the Tzibur check.

Taz (15): The Rema implies that letter of the law, it is permitted. A Mishnah teaches that one may not permit his own Bechor! R. Shimshon asked from other cases in which a Chacham may permit his own, and answered that he may do so when there was no Isur Muchzak. This explains why he may check after Shechitah, for there is Chezkas Heter, but it should be forbidden to slaughter, for while alive there is Chezkas Isur! It seems that the Heter is only to slaughter, since most who slaughter are experts, but he may not rule about his own animal.

Mahari ha'Levi (the Taz' brother, Teshuvah 17, brought in R. Akiva Eiger): If a butcher was certified by a Chacham, he may slaughter by himself and sell to others, like the Rambam and Rivash say. Also the Rosh (Chulin 1:24) says that the custom is not to rely on butchers. This implies that letter of the law, one may believe them even if they were not certified. The custom is not due to concern lest they sell a Terefah for their benefit. Rather, Chachamim enacted that the Chacham check the knife. Chachamim pardoned their honor only to those whom they certified.

Mahari ha'Levi (ibid.): One witness cannot overturn Chezkas Isur. A Shochet is different, since most who slaughter are experts. R. Shimon ben Gamliel (35a) says that Kohanim are not believed about (Mumim in) their own (Bechoros). This is because they were established to be suspected. We do not find anywhere that Yisre'elim were suspected to feed Terefos to others for their own benefit. This is why the Rema connotes that only some places do not rely on the Shochet to check.