"First-person inclusive" forms are ones that refer to both the first and second person. In that case, why call them "first-person" anything? Wouldn't it be equally logical to call them "second-person inclusive"? It isn't that there's a division within the first person into inclusive and exclusive forms -- that wouldn't mean anything. Is this just a historical convention, due to the fact that when speakers of a language without such an opposition encounter a language with one, they perceive its inclusive forms to correspond to their own "first-person plural"?
Or is it common for inclusive forms to somehow pattern more like first-person than like second-person forms, and if so how?
(I realize that you could ask similar questions about the term "first-person plural", since this usually doesn't refer to multiple speakers but to a speaker plus others, and about "second-person plural" when this refers not to multiple listeners but to a listener plus others. But those forms at least can refer to plural speakers or to plural listeners, while an inclusive form can never refer to the first person alone.)