Fasting For a Minor

The Mishna in Yoma (82a) as elucidated by the Gemorah says that there is a law to teach kids to fast by a few years before they become obligated in mitzvot training them to fast for a few hours.  The Ritvah in Sukkah (3a) proves from the Gemorah there that the mitzvah of chinuch is to have the minor fulfill the mitzvah with all of its details, it does not suffice to merely do chinuch on the general idea of the mitzvah.  The Steipler (Sukkah siman 28) asks if so, what is the point of doing chinuch for a few hours of fasting?

The Rambam in Shvesus Asor (2:10) brings this law, קָטָן בֶּן תֵּשַׁע שָׁנִים וּבֶן עֶשֶׂר שָׁנִים מְחַנְּכִין אוֹתוֹ לְשָׁעוֹת. כֵּיצַד. הָיָה רָגִיל לֶאֱכל בִּשְׁתֵּי שָׁעוֹת בַּיּוֹם מַאֲכִילִין אוֹתוֹ בְּשָׁלֹשׁ. הָיָה רָגִיל בְּשָׁלֹשׁ מַאֲכִילִין אוֹתוֹ בְּאַרְבַּע. לְפִי כֹּחַ הַבֵּן מוֹסִיפִין לְעַנּוֹת אוֹתוֹ בְּשָׁעוֹת. בֶּן אַחַת עֶשְׂרֵה שָׁנָה בֵּין זָכָר בֵּין נְקֵבָה מִתְעַנֶּה וּמַשְׁלִים מִדִּבְרֵי סוֹפְרִים כְּדֵי לְחַנְּכוֹ בְּמִצְוֹת  Rabbenu Manoach notes that the Rambam adds לְחַנְּכוֹ בְּמִצְוֹת and מדברי סופרים only regarding the full fast, not the partial fast.  He explains there is rabbinic mitzvah of chinuch to train a child to do a mitzvah and then there is another law of chinuch which is not a rabbinic commandment but it is something one should do to train their children to go in the right path.  The full fast is the mitzvah of chinuch, to instruct a minor to do the mitzvah.  The partial fast is just a a good training idea but not the rabbinic mitzvah of chinuch.  In the back of Rav Chayim on Shas the Briskor Rav says a similar idea to explain Rabbenu Yonah at the beginning of Berachot.  Rashi says that one does have to do chinuch for krias shema even for kids that have reached the age of chinuch.  Tosfos asks that the Gemorah Sukkah (42a) says that once a kid knows how to speak his father must teach him shema?  Rabbenu Yona answers that the Gemorah doesn't mean it is an obligation but rather that it is to teach the kids to do mitzvot.  What is this distinction?  The Rav explains with this yesod that there are two dinim of chinuch.  There is no rabbinic commandment of chinuch for krias shema but one should still teach there kid to be accustomed to doing mitzvot.  The Ritvah that says that the mitzvah must be done in all its details is referring to the mitzvah of chinuch, but the second din, to accustom a minor to know how to do mitzvot still applies even if not performed exactly correct.  

This law of training a minor to fast is only mentioned regarding Yom Kippur but not for other fasts.  The Briskor Rav (Kovetz Inyaninim Lbeis Brisk) questions why there is this distinction?  He explains the fast of Yom Kippur is different from that of other fast days.  The Rambam  (Lasw of Taanis 5:1) describes the purpose of the fasts is to arouse one to do teshuva.  Since teshuva is not applicable for a katan, there is no law of chinuch for a few hours.  However, the fast of Yom Kippur is for affliction and one can be be mechanach a katan in that mitzvah.