In Mishna 1 of of the Eighth Perek of Masechet Sanhedrin it states that we know the ages in which the halachot of ben sorrer u'moreh apply from the fact that the Torah says "ben" (boy) and not "ish" (man); the same Mishna also mentions that we learn they don't apply to a girl because it specifically says "ben" and not "bat" (girl).
However, in the Mishna, the two quotes are ordered such that "boy and not girl" comes first (directly after stating the age that the halachot apply) and "boy and not man" comes second. If (as the Yad Rama states) the main point which relates to the age is "boy and not man", and the "boy and not girl" is added because it is learned from the same phrase in the Torah, the order seems like it should be reversed. The fact that the order is as it is seems to suggest that "boy and not girl" teaches us something essential which we need to know in order to understand "boy and not man".
Why does "boy and not girl" come in the Mishna before the more relevant "boy and not man"?
If it is to teach us something about "boy and not man," what does it teach us?