Linguistically, the term “grammatical gender” is really a historical mistake based on linguistics the discipline being born in Indo-European languages, (twice – first with the first Sanskrit grammar, then for serious with people noticing suspiciously many similarities between Sanskrit and Latin)

The new and more inclusive term is “noun classes”, e.g. Swahili has nine, e.g. “mtu” is person, class “animate/human singular”, then you have “utu”, “humanity”, from the same root but in the class for abstractions. All Indo-European languages have three, and in that context “female gender” is really “the noun class that the word ‘woman’ is part of”, same for “man” and “thing”. Girl is neuter in German because it’s a diminutive and all diminutives are neuter, “person” is female and “human” male because that’s how the language assigned them semi-randomly to classes (mostly through phonetics). Nouns constructed with infinitive+er (like baker, very similar formation rules as in English) are all male, feminists really don’t like that because that covers basically all professions… but it also makes all murderers male. Which doesn’t make all murderers male, same as me being a person doesn’t make me female. Grammatical /= personal gender.

This is all that you can point to a chair (male) and table (female) and have a good chance to be able to refer to them very efficiently, like “his leg is broken” and it being clear that you don’t mean the table: That wouldn’t make any sense as it’s female and you’d say “her leg is broken”.