Luke said that Simeon, guided by the Holy Spirit (ἐν τῷ Πνεύματι), went into the Jerusalem Temple (καὶ ἦλθεν…εἰς τὸ ἱερόν). Then the parents of the child Jesus brought him into the Temple (καὶ ἐν τῷ εἰσαγαγεῖν τοὺς γονεῖς τὸ παιδίον Ἰησοῦν τοῦ ποιῆσαι αὐτοὺς) for the customary actions under the Law (κατὰ τὸ εἰθισμένον τοῦ νόμου περὶ αὐτοῦ). Unfortunately, there were no ordinary customs for the children, since the purification ritual was for the mother. It was rare for a mother to offer up her son to God. Normally, the 2 birds were sufficient as an offering for the first-born male child. Nevertheless, Simeon was there in the Temple when Mary, Joseph, and the child Jesus came into the Jerusalem Temple.
Luke said that when the time or the days were completed (Καὶ ὅτε ἐπλήσθησαν αἱ ἡμέραι) for their purification (τοῦ καθαρισμοῦ αὐτῶν), according to the law of Moses (κατὰ τὸν νόμον Μωϋσέως, Joseph and Mary brought Jesus to Jerusalem (ἀνήγαγον αὐτὸν εἰς Ἱεροσόλυμα) to present him to the Lord (παραστῆσαι τῷ Κυρίῳ). What is this purification and is it different than circumcision. The story of John did not have this purification ritual. Strictly speaking, this was a purification of the mother to take place 40 days after the birth of a child that had made her unclean as described in Leviticus, chapter 12:1-8. The presentation of the child and the father were not part of this purification ritual. There was no law or custom about the presentation of a child, other than the presentation of the first born as in Exodus, chapter 13:2 and 13:16. Women were considered unclean after childbirth because of the blood discharge that took place with birthing. If a male was born, the woman was unclean for 7 days, like menstruation, so that on the 8th day the male child could be circumcised. There were 33 more days of blood purification for the male child. During her unclean period, this new mother could not touch any holy thing, or go into the sanctuary. Thus, the purification ritual took place on the 40th day, a symbolic number based on the 40 years of the Israelites in the desert wilderness.
Yahweh, via Ezekiel, wanted them to purify the sanctuary on the 1st day of the 1st month. In other words, this would be a New Year’s Day activity. They were to take an unblemished bull and use him to cleanse the sanctuary at the start of the new year. The priest should take some of the blood from the sin offering and put it on the doorposts of the Temple, as well as the four corners of the altar ledge and the posts of the gate of the inner court. The priest was also supposed to do this same ritual on the 7th day of the month for anyone who sinned inadvertently by error or ignorance. This purification ritual of the first day of the first month of the year would make an atonement for the Temple, so that it would be purified.