The (currently accepted) answer by @OzzieOzzie is just plain wrong.
This has nothing to do with priesthood - but being a Rabbi
At this time, one had to be approximately 30 years of age to become a Rabbi. This recorded in the Code of Jewish Law (O.C. 581:1), which was being written at that time, along with the codification of the Talmud.
You can read more about this over at mi yodeya where the user GershonGold comments:
The Rashbam explains that at 30 one is worthy of leadership.... Orach Chaim 581:1 mentions that a Baal Tefila for the High Holy days should be at least 30. The Mishna Berura explains that at 30 one is humble and broken hearted.
Furthermore, in Jewish though, God had commanded people to "be fruitful and multiply" (you can read more about Talmudic ideas of this here and here), and although no one would want to forbid a man from becoming a Rabbi due to lack of being married and having children, it was strongly encouraged. Of course this required you to be of an age - mid to late twenties - whereby you at least had the opportunity to experience "first mitzvot of the Torah" (ie, "be fruitful and multiply"). (Reference: this is mentioned in Satlow's Jewish Marriage in Antiquity, but it's a big book and I'll have hunt it down later).
There are more reasons (such as having to have experienced a significant amount of life, etc). But ultimately one could not lead a Rabbinical school, nor lead services on one of the High Holy days unless they were 30.
Jesus - a Jewish Rabbi - would not have been accepted at all unless he was at that age.
The problem with the priesthood claim
Jesus' lineage shows him being of the tribe of Judah; He is in line for being king. He absolutely does NOT qualify as a priest, who are required to be sons of Aaron (ie, Levites).
The reference to Jesus as "High Priest" is clearly stated as something entirely separate from the Levitical regulations. Paul talks about this at length in Hebrews 5-7, and even the prophecies of the Messiah mention that Messiah would be a priest - but NOT of the sons of Aaron; Messiah would be "in the order of Melchizedek" (Psalm 110:4). In fact, Hebrews explicitly says Jesus was NOT of the Levitical order (Heb 7:11):
If perfection could have been attained through the Levitical priesthood—and indeed the law given to the people established that priesthood—why was there still need for another priest to come, one in the order of Melchizedek, not in the order of Aaron?
There are no such requirements for "being of the order of Melchizedek".
This distinction is crucial, because there are differences in the priesthoods. For example:
- there is no maximum: Levites aged-out at 50; there is no maximum age for being in the order of Melchizedek (which means Jesus can be a High Priest forever)
- the Levites were required to keep people away from God. Only the High Priest could enter God's presence (and then only one day a year). Anyone who tried was to be killed on-site (hence all the guards). But Jesus' role is to bring people into God's presence.
- the Levites were forbidden from being king, and Jesus is described as the King of Israel