The Chiddushei HaRim [the first Gerrer Rebbe] has a brilliantly simple answer. The first time Shabbos is presented to the Jewish people [in this weeks parsha - beshalach] the only melacha mentioned is הוצאה, as it says אל יצא איש ממקומו and the rabbis expound אל יוציא -don't do הוצאה. So of course the mishna began with הוצאה because that's what the Torah started with! [See sefer ליקוטי יהודה - it says more there but we tried to keep it digestible for all].
A shiur for Shabbos.
A delicious Shabbos:-)
