Says it all about that. Simply. Factually.

Well it's baked into the cake really...

A bar mitzvah (masc.) or bat mitzvah (fem.)[a] is a coming-of-age ritual in Judaism. According to Jewish law, before children reach a certain age, the parents are responsible for their child's actions. Once Jewish children reach that age, they are said to "become" b'nai mitzvah, at which point they begin to be held accountable for their own actions. Traditionally, the father of a bar or bat mitzvah offers thanks to God that he is no longer punished for his child's sins.

In Orthodox communities, boys become bar mitzvah at 13 and girls become bat mitzvah at 12. In most Reform, Reconstructionist, and Conservative communities, the milestone is 13 regardless of gender.[4] After this point, children are also held responsible for knowing Jewish ritual law, tradition, and ethics, and are able to participate in all areas of Jewish community life to the same extent as adults. In some Jewish communities, men's and women's roles differ in certain respects. For example, in Orthodox Judaism, once a boy turns 13, it is permitted to count him for the purpose of determining whether there is a prayer quorum, and he may lead prayer and other religious services in the family and the community.[5]

Bar mitzvah is mentioned in the Mishnah[6] and the Talmud. Some classic sources identify the age at which children must begin to participate in the ritual of fasting on Yom Kippur as 13 for boys and 12 for girls. The age of b'nai mitzvah roughly coincides with the onset of puberty.[7] The bar/bat mitzvah ceremony is usually held on the first Shabbat after the birthday on which the child reaches the eligible age.

Which begs the question: If they are considered an adult at 13, what for them, is considered a young adult (our 18)?

AJAP

Well, only if the kid is a goy.