The order of the wording of the Ben Sorrer U'Moreh source Mishnah

Question

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?

Answer 1

My guess is that the drasha of "בן ולא בת, בן ולא איש" was a known drasha that the mishna here is incorporating to support it's statement about the age of the ben sorrer u'moreh. Although the fact about "בן ולא בת" is not relevant to the discussion of the mishna, it includes the full statement as it was known.

To give a more famous example, in the gemara that discusses the eligibility of Ruth as a convert uses the drasha for support: "עמוני ולא עמונית, מואבי ולא מואבית". Why is the part about "עמוני" relevant? It's not. It was a known drasha that is being quoted in full as it was known to support a halachic statement.