The day we refer to as Simchat Torah in the Diaspora is actually the second day of the holiday of Shemini Atzeret so the question can be asked, both in the Diaspora and in Eretz Yisrael where the celebration of Simchat Torah is on the (only) day of Shemini Atzeret, why do we celebrate this occassion on a day that is already a holiday? In other words, why do we make the siyum of finishing the yearly reading of the Torah on this day? When one considers the idea that we are not to create another occasion of simcha (joy) on a holiday which has its own reason for joy, this question is even more potent. While we can technically argue that the making of a siyum does not technically violate the principle of mixing joys, the underlying thought is still most significant. Why not mark another day with the joy of the siyum of finishing the weekly readings of the Torah? Why specifically make this siyum on Shemini Atzeret?
There are many sides to this question. It may be something you want to ponder that may give you a greater appreciation of the nature of the day.
Rabbi Ben Hecht