Articles about the birth date of Christ sometimes state that it was an ancient teaching or understanding that the rabbis and other believed that the righteous died on their birth dates. While the claim is often made, I have rarely seen a reference given for this teaching.

So here are some references for the claim. I have arranged the text to make it easier to read and provided a fairly literal translation and references for the quotations.

The rabbinic tradition that a righteous man would die on the day he was born seems to be fairly early. The foundational passage is Exodus 23:26. This passage in context with Moses' use of the word "today" in Deuteronomy 31:2 form the main argument of the tradition.

Sotah 13b

Sotah שׂוֹטָה is one of the tractates of Seder Nashim “Order of Women”. Seder Nashim concentrates on family law. Tractate Sota discusses the laws relating to a woman who is suspected of adultery. The word sotah refers to a woman who is tried for adultery under biblical law.

״וַיֹּאמֶר אֲלֵיהֶם

בֶּן מֵאָה וְעֶשְׂרִים שָׁנָה אָנֹכִי הַיּוֹם״,

שֶׁאֵין תַּלְמוּד לוֹמַר ״הַיּוֹם״:

הַיּוֹם מָלְאוּ יָמַי וּשְׁנוֹתַי.

לְלַמֶּדְךָ שֶׁהַקָּדוֹשׁ בָּרוּךְ הוּא

מַשְׁלִים שְׁנוֹתֵיהֶם שֶׁל צַדִּיקִים

מִיּוֹם לְיוֹם וּמֵחֹדֶשׁ לְחֹדֶשׁ,

דִּכְתִיב:

״אֶת מִסְפַּר יָמֶיךָ אֲמַלֵּא״.

And he said to them:
“I am one hundred and twenty years old today…” (Dt. 31:2)

As it is not necessary for the verse to say “today”
    “this day my days and years have been filled
         to teach you that the Holy One, blessed be He,
             orders the years of the righteous

from day to day and month to month.”

As it is written:
“The number of your days I will fill.” (Exodus 23:26)

The Aramaic text is from the Davidson Edition at Safira.

https://www.sefaria.org/Sotah.13b.16-17?lang=bi

Kidushin 38a

Kiddushin קִידּוּשִׁין “Betrothal” is the final tractate in Seder Nashim. As the title expresses, it deals primarily with legal issues related to engagement and marriage.

תַּנְיָא אִידַּךְ:

בְּשִׁבְעָה בַּאֲדָר מֵת מֹשֶׁה,

וּבְשִׁבְעָה בַּאֲדָר נוֹלַד.

מִנַּיִן שֶׁבְּשִׁבְעָה בַּאֲדָר מֵת –

שֶׁנֶּאֱמַר: ״וַיָּמׇת שָׁם מֹשֶׁה עֶבֶד ה׳״,

וּכְתִיב: ״וַיִּבְכּוּ בְנֵי יִשְׂרָאֵל אֶת מֹשֶׁה בְּעַרְבֹת מוֹאָב שְׁלֹשִׁים יוֹם״,

וּכְתִיב: ״וַיְהִי אַחֲרֵי מוֹת מֹשֶׁה עֶבֶד ה׳״,

וּכְתִיב: ״מֹשֶׁה עַבְדִּי מֵת וְעַתָּה קוּם עֲבֹר״

וּכְתִיב: ״עִבְרוּ בְּקֶרֶב הַמַּחֲנֶה וְצַוּוּ אֶת הָעָם

לֵאמֹר הָכִינוּ לָכֶם צֵדָה כִּי בְּעוֹד שְׁלֹשֶׁת יָמִים תַּעַבְרוּ אֶת הַיַּרְדֵּן״

וּכְתִיב: ״וְהָעָם עָלוּ מִן הַיַּרְדֵּן בֶּעָשׂוֹר לַחֹדֶשׁ הָרִאשׁוֹן״,

צֵא מֵהֶן שְׁלֹשִׁים וּשְׁלֹשָׁה יָמִים לְמַפְרֵעַ,

הָא לָמַדְתָּ שֶׁבְּשִׁבְעָה בַּאֲדָר מֵת מֹשֶׁה.

It is taught again

Moses died on the seventh of Adar,

and he was born on the seventh of Adar.

From where is this that on the seventh of Adar he died?

As it is stated:

“And Moses the servant of the Lord died there…” (Dt 34:5)

And as it is written:

“And the children of Israel mourned Moses in the plains of Moab for thirty days.” (Dt 34:8)

And as it is written:

“And so it was after the death of Moses, the servant of the Lord…” (Jos 1:1)

And as it is written:

“Moses my servant is dead. Now you arise and cross over…” (Jos 1:2)

And as it is written:

“Pass through the middle of the camp and command the people

saying: ‘Prepare your provisions for in yet three days you will cross the Jordan…’” (Jos 1:11)

And as it is written:

“And the people went up from the Jordan on the tenth day of the first month…” (Jos 4:19)

Go back from them thirty three days
[30 for the mourning of Moses
and 3 for the preparation to cross the Jordan]

thus you learn that it was on the seventh of Adar that Moses died.

וּמִנַּיִן

שֶׁבְּשִׁבְעָה בַּאֲדָר נוֹלַד מֹשֶׁה –

שֶׁנֶּאֱמַר:

״וַיֹּאמֶר אֲלֵהֶם

בֶּן מֵאָה וְעֶשְׂרִים שָׁנָה אָנֹכִי הַיּוֹם

לֹא אוּכַל עוֹד לָצֵאת וְלָבוֹא״,

שֶׁאֵין תַּלְמוּד לוֹמַר ״הַיּוֹם״,

מָה תַּלְמוּד לוֹמַר ״הַיּוֹם״?

מְלַמֵּד שֶׁהַקָּדוֹשׁ בָּרוּךְ הוּא

יוֹשֵׁב וּמְמַלֵּא שְׁנוֹתֵיהֶם שֶׁל צַדִּיקִים מִיּוֹם לְיוֹם וּמֵחֹדֶשׁ לְחֹדֶשׁ,

שֶׁנֶּאֱמַר: ״אֶת מִסְפַּר יָמֶיךָ אֲמַלֵּא״.

And where does is come from
that Moses was born on the seventh of Adar?

As it is stated:
“And he said to them:
‘I am one hundred and twenty years old today.
I am not able again to go out or to come in…” (Dt 31:2)

Since there is no need for the verse to say “today”

what [reason does] the verse say “today”?

This teaches that the Holy One, Blessed be He, sits and fills up the years of the righteous from day to day and from month to month.

As it is stated: “The number of your days, I will make full.” (Ex 23:26)

https://www.sefaria.org/Kiddushin.38a.5-6?lang=bi&with=all&lang2=en

Megillah 13:b

Megilla is the 10^th tractate in the second order of the Misha: Seder Moed “The Order of Festival”. The title is Masekhet Megilla מסכת מגילה "Tractate Scroll” and deals with legal issues, customs, and stories relating to Purim.

״הִפִּיל פּוּר הוּא הַגּוֹרָל״,

תָּנָא: כֵּיוָן שֶׁנָּפַל פּוּר בְּחוֹדֶשׁ אֲדָר

שָׂמַח שִׂמְחָה גְּדוֹלָה,

אָמַר:

נָפַל לִי פּוּר בְּיֶרַח שֶׁמֵּת בּוֹ מֹשֶׁה.

וְלֹא הָיָה יוֹדֵעַ

שֶׁבְּשִׁבְעָה בַּאֲדָר מֵת,

וּבְשִׁבְעָה בַּאֲדָר נוֹלָד.

They cast the Pur, that is, the lot” (Esther 3:7)

He [a sage] taught:

“Once the lot fell in the month of Adar

he [Haman] greatly rejoiced.

He [Haman] said:

“The lot has fallen for me in the month that Moses died.”

He [Haman] did not know that

it was on the seventh of Adar he died,

and it was on the seventh of Adar he was born.”

This interpreter is saying that a special cause for Haman’s rejoicing about the lot is that the month of Adar was chosen. Haman was especially joyful because, according to this interpreter, Haman knew that was the same month Moses died. So the people of Moses would be exterminated in the same month Moses himself died. But what Haman did not know is that Moses was also born that same month. The irony being that instead of dying, the people would be renewed. This would become a time of rejoicing for the people.

https://www.sefaria.org/Megillah.13b.15-16?lang=bi

Rosh HaShana 11a

Rosh Hashana רֹאשׁ הַשָּׁנָה is the eighth tractate of Seder Moed. The primary focus is the calendar year and the correct reckoning of time in accordance with Scripture.

מַאן דְּאָמַר בְּנִיסָן נוֹלְדוּ — בְּנִיסָן מֵתוּ.

מַאן דְּאָמַר בְּתִשְׁרִי נוֹלְדוּ — בְּתִשְׁרִי מֵתוּ,

שֶׁנֶּאֱמַר:

״וַיֹּאמֶר אֲלֵיהֶם

בֶּן מֵאָה וְעֶשְׂרִים שָׁנָה אָנֹכִי הַיּוֹם״,

שֶׁאֵין תַּלְמוּד לוֹמַר ״הַיּוֹם״,

וּמָה תַּלְמוּד לוֹמַר ״הַיּוֹם״ —

הַיּוֹם מָלְאוּ יָמַי וּשְׁנוֹתַי.

לְלַמֶּדְךָ שֶׁהַקָּדוֹשׁ בָּרוּךְ הוּא

יוֹשֵׁב וּמְמַלֵּא שְׁנוֹתֵיהֶם שֶׁל צַדִּיקִים

מִיּוֹם לְיוֹם מֵחֹדֶשׁ לְחֹדֶשׁ,

שֶׁנֶּאֱמַר: ״אֶת מִסְפַּר יָמֶיךָ אֲמַלֵּא״.

The one who said they were born in Nisan says in Nisan they died.

The one who says they were born in Tishrei says in Tishrei they died.

As it is said:

“And he said to them,

‘I am one hundred and twenty years old today.’” (Dt 31:2)

As it is not necessary for the verse to say, “today”,

And what [reason] does the verse say, “today”?

“Today my days and years are filled.”

[This is] to teach you that the Holy One, Blessed be He,

sits and fills the years of the righteous

from day to day and from month to month.

As it is said: “The number of your days I will fill.” (Ex 23:26)

https://www.sefaria.org/Rosh_Hashanah.11a.17?lang=bi

Rashi on Deuteronomy 1:3

Rashi is an acronym for Rabbi Shlomo Yitzchaki. He lived from about 1040 to 1105. Rashi is considered one of the foremost exegetes of the middle ages. He lived long after the Christian liturgical cycles had been established. Rashi has been widely respected for his knowledge of tradition, his expertise in Scripture, and his knowledge and application of rabbinical law. There are two comments he made in his commentary on Deuteronomy that are relevant to our discussion because Rashi shows how thoroughly established the birth day, death day tradition had been.

וַיְהִי֙ בְּאַרְבָּעִ֣ים שָׁנָ֔ה

בְּעַשְׁתֵּֽי־עָשָׂ֥ר חֹ֖דֶשׁ בְּאֶחָ֣ד לַחֹ֑דֶשׁ...

מְלַמֵּד שֶׁלֹּא הוֹכִיחָן אֶלָּא סָמוּךְ לַמִּיתָה;

מִמִּי לָמַד?

מִיַּעֲקֹב, שֶׁלֹּא הוֹכִיחַ אֶת בָּנָיו אֶלָּא סָמוּךְ לַמִּיתָה,

אָמַר, רְאוּבֵן בְּנִי אֲנִי אוֹמֵר ...

“And it came to pass in the fortieth year,

in the eleventh month, on the first of the month.”

He [Moses] teaches that one should not reprove unless one is close to death.

From whom did he learn?

From Jacob, who did not reprove his son until he was close to death.

“He said, ‘Reuben, my son, I have to say …’”

Deuteronomy 1:3 establishes the time of year in which Moses addressed the people of Israel. The eleventh month was later known as Adar. As we have seen in the preceding discussion, the context of Deuteronomy gives enough chronological information.

A discussion on the topic of withholding serious reproof until just before one’s death is found in the opening of Midrash Sifrei Devarim which was composed sometime around A.D. 200.

https://www.sefaria.org/Rashi_on_Deuteronomy.1.3.1?lang=bi