A part of the Insai school was called "Toryu" (meaning sect for the Shogunate family) because the grant master of Edo-Insai school was teaching archery for Tokugawa Shogunate family.
一部の印西派を当流と呼ぶのは、江戸印西派の宗家が徳川将軍家の弓術指南役だった事からで、将軍家の流派という意味。