Rabbi Kagan was born on January 26, 1838 in Dzyatlava, a town that was in those days part of the Russian Empire (nowadays in Belarus). His parents were Rabbi Aryeh Zev and Dobrusha Kagan. When he was nine years old, his father brought him to Vilnius to study in the yeshiva that Rabbi Chaim Nachman Parnes ran. His father was a teacher in the yeshiva as well. Rabbi Kagan's father died when he was eleven years old. His mother married a second husband, whose name was R' Shimon, and their family moved to Radun where R' Shimon came from. Rabbi Kagan married R' Shimon's daughter, whose name was Freida.