Nowhere in scripture does it say that Jesus took up the trade of his father. In fact, the absence of of any writing about his life from 13-30 would lead an Israelite reader to assume that he DID have formal rabbinic training, and rather, the verse here is a blatant statement from John that Jesus did not, however, state his first teaching on any other rabbi's teaching to validate his statement.
When a rabbi would begin his teaching years, he would never teach on his own merit. He would constantly quote his authorities. Jesus doesn't do this and it it was shocking. He stands on his own authority from his very first words, which in tradition was, again, unheard of. You had to earn that stature from years of proving yourself first in Rabbinical learning structure, then in teaching from the masters who'd gone before you. THEN if you gained reputation through the years, you could add your own commentary that diverged from the past and/or added to it.
When we look at the culture and tradition in which the gospels were written, it seems that the most logical assumption (for that is all we can make, is educated guesses on what happened in those 15-20 years) is that Jesus was in fact a trained Rabbi. This is beautiful. From age 12 he was so in tuned with the Father that he was asking rabbis intelligent questions in the temple and then told his mom that that's where he was supposed to be. Asking questions was not the same format as question asking we think of today. Question asking was not what people who didn't understand did, its what the TEACHER did to stimulate pensive thought, discussion and debate. His questions were stumping the Rabbis in the temple at age 12. THAT was immediate reason to be recruited by them for education. His parents would have been rebuked if they denied a child of this intellect this path.