Commentary for Bekhorot 2:8
אַחַת בִּכְּרָה וְאַחַת שֶׁלֹּא בִכְּרָה וְיָלְדוּ שְׁנֵי זְכָרִים, אֶחָד לוֹ וְאֶחָד לַכֹּהֵן. רַבִּי טַרְפוֹן אוֹמֵר, הַכֹּהֵן בּוֹרֵר לוֹ אֶת הַיָּפֶה. רַבִּי עֲקִיבָא אוֹמֵר, מְשַׁמְּנִין בֵּינֵיהֶן, וְהַשֵּׁנִי יִרְעֶה עַד שֶׁיִּסְתָּאֵב. וְחַיָּב בַּמַּתָּנוֹת. רַבִּי יוֹסֵי פּוֹטֵר, שֶׁהָיָה רַבִּי יוֹסֵי אוֹמֵר, כֹּל שֶׁחֲלִיפָיו בְּיַד כֹּהֵן, פָּטוּר מִן הַמַתָּנוֹת. רַבִּי מֵאִיר מְחַיֵּב. מֵת אֶחָד מֵהֶן, רַבִּי טַרְפוֹן אוֹמֵר, יַחֲלוֹקוּ. רַבִּי עֲקִיבָא אוֹמֵר, הַמּוֹצִיא מֵחֲבֵרוֹ עָלָיו הָרְאָיָה. זָכָר וּנְקֵבָה, אֵין כָּאן לַכֹּהֵן כְּלוּם:
If one ewe has given birth before and one has not, and they give birth to two males, one goes to [the owner], and the other goes to the priest. Rabbi Tarfon says: The priest chooses the better one. Rabbi 'Akiva says: We compromise. The second one goes out to graze until it develops a blemish, and it is obligated regarding the [priestly] gifts. Rabbi Yossi exempts it because Rabbi Yossi says: When the exchange goes to the priest, [the other animal] is exempt from the [priestly] gifts. Rabbi Meir obligates it. If one of them dies, Rabbi Tarfon says: They divide [the value of the remaining one]. Rabbi 'Akiva says: One who comes to extract from one's friend has the burden of proof. [If they give birth to] a male and a female, the priest receives nothing.
English Explanation of Mishnah Bekhorot
The second one [in the Israelite's possession] is left to pasture until it becomes blemished and the owner is liable for the [priest's] gifts. Rabbi Yose exempts him. For Rabbi Yose says: wherever the priest receives [an animal] in its place, he is exempt from the priestly gifts. Rabbi Meir however makes him liable.
If one of them died: Rabbi Tarfon says: they divide [the living one]. Rabbi Akiva says: the burden of proof is upon the claimant.
If they gave birth to a male and a female, the priest receives nothing [in such circumstances].
This mishnah is a continuation of yesterday and the previous day’s mishnah. Much of the explanation for the mishnah can be found there.
Section one: Again, we have here a situation where we know that one of two males is a first-born and one is not. One goes to the priest and again Rabbi Tarfon and Rabbi Akiva argue about how we determine who gets which animal. See mishnah six for an explanation.
Section two: Most of this section is the same as in mishnah six. We learn here, finally, the reason that Rabbi Yose exempts the animal that stays with the owner from being liable for the priestly gifts. Whenever a priest receives one animal in return for another, the animal that is exchanged is exempt. In this case the priest receives one animal in return for giving away the other animal. It is as if he received the animal and then exchanged it for another. Any animal owned by a priest is exempt from the priestly gifts, and therefore the animal that goes to the original owner is exempt. Rabbi Meir disagrees and says that he is still liable.
Sections three and four: These are the same as the end of mishnah six. See there for an explanation.