"I wanted to ask your opinion about an article I wrote on the 'age of accountability.' At age 12, Jesus is referred to as a 'boy/child,' and the (little) girl he raises from the dead is also referred to as '(little) girl/child' [Luke 2:43; Mark 5:41]. So, if the Bible refers to someone age 12 as a boy/girl, and in Acts we only see people getting baptized who are at least young men/women, wouldn't it stand to reason that we should not baptize anyone under the age of 13? Further, considering that the Bar Mitzvah age for boys is 12 and girls is 12/13, plus the fact that puberty generally starts around that age, can't we conclude from scripture, (Jewish) culture, and anatomy, that one cannot be considered a candidate for baptism until age 13? Please advise."
While a Greek word may refer to a 12-year-old, you haven't demonstrated that it couldn't also refer to a somewhat older child. Now of course you are right that puberty affects spiritual awareness, and few are ready at age 11, yet there are too many clear exceptions for your thesis to work. Many are ready before the teen years…. And maybe some in their late teens still lack the maturity to repent. As for puberty, some "late developers" might even be ready sooner than younger kids who are maturing sooner.
I used to think that experience of puberty was necessary for an informed decision about Christ -- that the children needed to be 15 (14 at the youngest) before they were ready. Some years later, an older (wiser) brothers talked me out of my position. I especially recall an elder explaining that all three of his daughters were baptized at 13. In time, I was meeting men and women whom I considered to be true Christians who became Christians (in a few cases) even before their 12th birthday.
If you admit there are exceptions, then instead of a proof all you have noted is an observation: that adolescents are more prepared to make adult decisions than younger children. It's more a truism than a significant truth.
Further, can you imagine the anxiety, feigned faith, parental pressure, and other negative effects if the Bible specified the age at which we could become Christians? Those who needed more time might be under unfair pressure. Those who were advanced might be deprived of salvation. Repentance would be all about meeting a deadline, instead of truly trusting the Lord with our lives.
If there were a rule, or a boundary, or dividing line, the Lord would have made this clear — this is important! Possible implications are not the same as hard proof. If you have stronger reasons, please write again and I will be happy to consider them.
Our inability to nail down an exact age of accountability isn't necessarily a crisis of theology or failure in our thinking. The Lord knows when the younger folks are ready, and it seems pretty clear they mature at different rates and times. Maybe this will help. There is an analogy in the process of wandering away from Christ (James 5:19-20). At some point, there is a very real chance the person could fall away -- that is, cross the point of no return (Heb 6:4-6). God knows when a person is too far gone ("broken") and cannot come back (Prov 29:1). Just because we can't necessarily know when that time is doesn't mean that it can't happen. The Lord knows; we leave it in his hands.