6 Iyar (Emor & Sefira)

The Torah says start counting Sefiras Ha'omer (Vayikra 23,15) "Mimacharas Hashabbos" (after shabbos) and Rashi says it means after the first day of Yom Tov of Pesach because Yom Tov is often called Shabbos. Why doesn't the Torah say the actual date that we start counting Sefiras Ha'omer is the second day of Pesach or the 16th of Nissan? There's no gain of calling it after the Shabbos, all it does is give room for people to make the mistake of thinking it actually means after Shabbos (as the Tziddukim did), so why not say the real date?