Rabbi Nachman revealed that the Matza brings the highest da'as (cognizance/intelligence). With this higher da'as comes peace, for anger is caused by small mindedness, and the greater the da'as the more peace. Rabbi Nachman revealed that the highest da'as and peace is argumentation for the sake of Heaven - Machlokes LiShaim Shumayim. With this we can provide another reason why we make the blessing of eating Matza on the broken Matza - to indicate that we are hoping to achieve the highest peace with this small piece which was broken (an aspect of "machlokes").
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Great blessings of Na Nach Nachmu Nachman Meuman!