the original meaning of "gender" (in latin) was "kind" (but also "kin" (a cognate, actually), so there was always a shade of meaning relating to reproduction there).

by the time romans started writing about their grammar, latin had lost its third noun class (i think very originally it also had m/f/n, like germanic languages). so i think already with the romans the concepts of noun class and social gender and sex got confused with each other a bit. at any rate, the romans found latin to have two noun classes, and words like mother and girl belonged to class A, while father and boy belonged to class B, so they ran with that, and called the two classes m and f. and it stuck.

and so in european languages, whose grammars were all written down by people familiar with latin grammar, the conflation was carried forward (and also because european languages often have a noun class system that maps to m/f somewhat).

so it's eurocentrism, in a way, but even within europe, it takes a lot of handwaving to sustain this idea, because apart from words for people and animals, pretending that social gender and grammatical gender are the same concept is difficult.

but yes, grammatical gender is just an arbitrary grouping of nouns into classes. which is why i like the term "noun class" better.

anyway, i think a bit too much is made of grammatical gender, in the sense that it's just as possible to be breathtakingly sexist in a language with no grammatical gender, so it's clearly not a very important cog in the great wheel of oppression.