Rashi explains that the terms “father” and “brother” used in the pasuk does not refer to the Levi’s real father or brother, since no member of the tribe of Levi had sinned. He, therefore, suggests that these terms refer to their mother’s father or a brother from the same mother who, in either case, was a Yisrael. If this is the case, why does the Torah emphasize the words father and brother?
Horav Nissan Alpert, z.l., suggests the following thought. The Leviim killed the sinners because of their zealousness for the sake of Hashem’s Name. One might hypothesize that they had done this only because they had no relationship to the sinners and, therefore, no special sensitivity towards them. The Torah responds by viewing these sinners as family. The love of the Leviim for each and every Jew was tantamount to a family relationship. They considered every Jew to be their brother; every elder was considered their father! Nonetheless, when Moshe issued the command for avenging Hashem’s Name, they responded immediately. Their love for Hashem transcended even their sensitivity towards their brethren.