A better argument would be a language that has no word for male or female. Shouldn't there be some language, where, maybe, the words "man" and "woman" are the same & the difference only designated by context? If not, that would be an argument in my favor. If there is - and such languages are common - that would be an argument in your favor.
That's...literally what I just said. Neither of those languages distinguish between genders.
ia can mean "he", "she" or "it".
ipo means both boyfriend
and girlfriend, etc. This isn't even that rare of a phenomenon in linguistics. None of the languages from the Austronesian, Uralic, or Turkic language families have gender. The Swahili language distinguishes between 18 different noun classes (genders, if you will), and none of those noun classes are tied to sexual gender. If a language does have gender, it's because their parent language did, and in the case of IE languages, that came about as a result of the need to create abstract forms resulting in a splitting of the inanimate class into two morphological paradigms.¹ It's also worth noting, that one notable exception exists in the IE family, viz. Hittite, in which there is only masculine and neuter genders; no feminine.
I mean, the IE languages also originally distinguished between singular,
dual, and plural. It's understandable why it might develop - we have two arms, two eyes, two legs, two hands, and two birth-parents, but that doesn't mean that the dual form is an intrinsic, natural, or necessary function of every language system everywhere.
¹An example of how this might work: opus (gen. operis) = artistic work. opera = plural form. New art form develops in which writing (story) and music and stage design are fused into one whole, opera (gen. operum). What do you do if you want to talk about more than one opera though? You invent a new noun class in which -a is the singular, and then develop endings that follow the same paradigmata of the other two classes.