This phrase originates from Iggeret HaKodesh (part of the Tanya by the Alter Rebbe, Rabbi Schneur Zalman of Liadi), specifically in Chapter 22.
Explanation of the difference:
In the first instance, the father is described as merciful, wise, and righteous, but when acting as an advocate, the description adds the term "pious" (חסיד) as well.
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The first description (merciful, wise, and righteous) relates to the father acting in his disciplinary role, striking his son. This emphasizes qualities necessary for judgment and discipline: mercy to balance severity, wisdom to understand the proper measure of punishment, and righteousness to ensure fairness and justice.
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The second description (merciful, righteous, and pious) refers to the father acting as an advocate, interceding on behalf of his son. In this role, the father also needs the attribute of piety (חסיד), which transcends strict justice and mercy. Piety represents a higher level of compassion and kindness, going beyond the letter of the law, reflecting a deeper, selfless desire to advocate and bring about forgiveness or leniency.
Thus, when the father acts as a disciplinarian, he requires wisdom and righteousness, but when he acts as an advocate, he requires not only mercy and righteousness but also piety, symbolizing his elevated kindness and devotion to his son's well-being.