I see some discussion on Trope and the cantillation symbols, but little has been addressed by way of why you lein. I read Deuteronomy 31:29 in Scripture today and it made me wonder, Is it possible that in your heritage Torah has always been sung and that this verse is why Torah leining is taught to your children?
I had always thought the song here referred to only a portion in Deuteronomy. But I saw Deuteronomy 31:29 cited as the reason you copy your own torah scrolls, and it connected Torah leining with this verse in my mind. I imagine, that if Moses turned any portion of it into song you would remember it throughout your generations, song just does that!
וְעַתָּה, כִּתְבוּ לָכֶם אֶת-הַשִּׁירָה הַזֹּאת, וְלַמְּדָהּ אֶת-בְּנֵי-יִשְׂרָאֵל, שִׂימָהּ בְּפִיהֶם: לְמַעַן תִּהְיֶה-לִּי הַשִּׁירָה הַזֹּאת, לְעֵד--בִּבְנֵי יִשְׂרָאֵל.
וַיִּכְתֹּב מֹשֶׁה אֶת-הַשִּׁירָה הַזֹּאת, בַּיּוֹם הַהוּא; וַיְלַמְּדָהּ, אֶת-בְּנֵי יִשְׂרָאֵל.
I was wondering if this was WHY you lein and why leining Torah is part of preparing your children for bar mitzvah and bat mitzvah--helping them become sons of commandment and and daughters of commandment.