הַחדֶשׁ הַזֶּה לָכֶם ראשׁ חֳדָשִׁים רִאשׁוֹן הוּא לָכֶם לְחָדְשֵׁי הַשָּׁנָה.
The word לָכֶם has the same letters as מלך, king. This, the Kav Hayashar says, alludes to Nisan being the first and “king” of all the months.
The Degel Machane Ephraim quotes the first mishna in Rosh Hashona: the first of Nisan is Rosh Hashona of Malochim, and it is know that only Klal Yisroel is called Bnei Malochim. Therefore, it says הַחדֶשׁ הַזֶּה לָכֶם – לָכֶם has the same letters as מלך. This month, which is Rosh Hashona of Malochim is given specifically to Klal Yisroel.