במדבר פרק א, ב ש ְאוּ אֶּת-רֹאש כָֹּל -עֲדַת בְּנֵי-יִּש ְרָֹ אֵל לְמִּש ְפְּחֹתָֹם לְבֵית אֲבֹתָֹם
מסכת בבא בתרא דף קט/ב משפחת אב קרויה משפחה משפחת אם אינה קרויה משפחה
Simply the males build the material aspects of civilization, and are thus called “builders” (בנים). As stated in Bereshis 5, 28, “a son was born to him that built the world”. And as the Ralbag explains a still-born baby is not called בן, since the baby did not have a chance to build the world.
Many practical differences deriving in one’s family heritage being from the father and not the mother. Maternal-only brothers and sisters do not inherit one another. Only paternal family members are responsible to redeem someone that was sold into slavery.
This concept can also assist in understanding the principle עמוני ולא עמונית מואבי ולא מואבית (this seasonal time of reading the book of Rus). The exclusion exists only for the males, since they are the main component of that civilization (that was banned from converting to the Jewish nation).
Also, the law recognizes greater responsibility to paternal family members in matters of charity and chalitzah.
Alternatively, the Gemara (Kiddushin 68b) states that maternal-only brothers have greater love for one another than paternal-only brothers.
