(Native Spanish speaker, Also learned Greek for 13 years)
In Spanish, "person" is "persona". It ends in -a, so it's feminine. This has nothing to do with the gender of the person in question. Every person is a persona. You don't call men "*persono", because that's not a word.
In Greek, boy (αγόρι) and girl (κορίτσι) are neuter because they end in -ι.
Keys don't change gender if I change language (las llaves (feminine), τα κλειδιά (neuter), the keys (N/A)), the only thing that changes is the word(s) used to refer to them.
saying grammatical gender is about the object itself and not just its word is like saying there's something different between the actions "πάω" and "πηγαίνω" JUST because they're in different verb genders (-άω vs -ω), despite the fact they're literally the same thing. They both mean "I go". No nuanced little differences between the two, they are literally the same.
The word for chair in Spanish (silla) is feminine because it just happened to go into that category. Nothing about the chair itself is feminine.
After all, it's Grammatical gender. Grammar applies to words, not objects.