In Luke 2:22, it is written,
And when the days of her purification according to the law of Moses were accomplished, they brought him to Jerusalem, to present him to the Lord; KJV, 1769
Καὶ ὅτε ἐπλήσθησαν αἱ ἡμέραι τοῦ καθαρισμοῦ αὐτῶν κατὰ τὸν νόμον Μωσέως, ἀνήγαγον αὐτὸν εἰς Ἱεροσόλυμα παραστῆσαι τῷ κυρίῳ TR, 1550
Why does the KJV translate the Greek phrase «τοῦ καθαρισμοῦ αὐτῶν» into English as “her purification” rather than “their purification”?
This is a textual issue. Most important manuscripts (including Sinaiticus, Alexandrinus, and Vaticanus) contain αὐτῶν, unambiguously 3rd masculine plural (genitive). This is the reading of the Textus Receptus that you quote However, the Vulgate contains eius, the 3rd person singular genitive pronoun that may be either masculine or feminine. This reading, as well as the one late miniscule that contains the unambiguous Greek 3rd feminine singular αὐτῆς (Codex 76), were presumably motivated by copyists’ awareness that purification laws applied to women only.
The KJV here appears to be following the sixteenth century text of Theodore Beza, who revised Erasmus’ Textus Receptus. Although the reading αὐτῆς is not found in the TR, Beza most likely elected to revise the TR by the same logic outlined above, supported by the fact that this reading is allowed by the Vulgate.
The textual situation is laid out with clarity in the NET translation notes.
The difficulty of the reading αὐτῶν is that, by Levitical law, only the mother required purification rites. (See Lev. 12:6 re. יְמֵ֣י טָהֳרָהּ | αἱ ἡμέραι καθάρσεως αὐτῆς.) According to one commentator:
It is most likely that Luke has run together the cleansing of the mother and the offering of the child...into one act....
I. Howard Marshall, The Gospel of Luke: a Commentary on the Greek Text (NIGTC). Grand Rapids: Eerdmans, 1978), pp 115-116.
There is zero Greek manuscript that attest the feminine pronoun here "her purification", as adopted by KJV through Beza's edition and the Complutensian Polyglot, both of the 16th century. This means in some of the Textual errors in the KJV represent corruption as recent as the 16th century. The apparatus in the Critical Greek editions wrongly show the variant αὐτῆς noting codex 76. But as Hatch explains, 76 does not read αὐτῆς.
“Codex 76, a Vienna manuscript of the twelfth or thirteenth century, is commonly cited as a witness for αυτής. This, however, is an error; for Gregory, who examined the codex in 1887, reports that it reads αυτών in Luke 2,22 (cf. Tischendorf, Novum Testamentum Greece, HI, 484). Codex 76 is one of the manuscripts consulted by Alter. He printed αυτής in Luke 2, 22 without recording the reading of this codex. Griesbach inferred from Alter's silence that αυτής was found in 76, and in order to indicate that the citation was based on inference he enclosed the number 76 in parentheses. It has been pointed out above that this manuscript really has αυτών; and Alter failed to indicate this fact through carelessness. His edition is substantially a reprint of 218, a thirteenth century codex in the Imperial Library in Vienna. Professor Karl Beth, of Vienna, has kindly informed me that it reads αυτών in Luke 2, 22. Alter, a Roman Catholic scholar, no doubt adopted αυτής from the Complutensian-Elzevir tradition, or possibly from the Vulgate eins. Scholz, with characteristic inaccuracy, omitted Griesbach's parentheses about 76, and thenceforth αυτής passed into the critical tradition as the true reading of the manuscript.”
William Henry Paine Hatch, “The Text Of Luke II, 22.,” Harvard Theological Review 14, no. 4 (1921): 380, note 4.
The motivation of the interpolation from the plural to "her" is to be understood solely as a theological agenda to protect Jesus from any impurity, as admitted by Alfred Plummer (Luke ICC commentary) and which is demonstrated by all devotees even to this day.
