A. Talmud Rosh Hashanah 2b learns it from a juxtaposition of Shlomo’s royal reckoning and the reckoning from the Exodus. Rabbeynu Nissim explains this is because there would never be a Jewish King if we hadn’t left Egypt. In the language of the Haggadah “if G-d would not have taken us out then, we would still be slaves to Pharaoh in Egypt.”
From a Chassidic perspective, an ideal Jewish king is a quality leader with spiritual inspiration and connection to G-d. This explains why Samuel was reluctant to appoint a king when the Jews asked for one, even though the Torah itself encourages us to have a king. For the Jews of Samuel’s time asked for a King “like all other nations” which is very different from what an ideal Jewish king should be about – and that ideal is worth celebrating in the month of Nissan, when we became the Jewish nation.