There's actually a lot of interesting info on this stuff in linguistics, I'm sure you could find some good books on the subject. My memory of linguistics is rusty at the moment, but many of these things aren't nearly as sexist as they may seem. In particular, grammatical gender is often more of a "sorting" system from what I recall, and helps mark certain discourse syntax in language. In fact, "gender" in languages like Spanish is better termed as Noun Classes. Many languages have Noun Classes, the biggest one aside from Gender being Animate/Inanimate (actually might be more languages than this). The European languages, in general, are more heavily focused on that type of Gender marking. Just take a look at Navajo. I believe that one has some crazy amount of Noun Classes (which are what Gender is in languages like Spanish, where the word's inflection changes based off the gender).
I believe they have shown that gender in languages that assign it like Spanish, such as to tables or tvs, does affect speaker perceptions of something being more masculine or feminine, but I'm not a 100% sure on that, and I don't believe it's very significant.
For gender referring to family terms, such as your Chinese example, I would speculate this does come from a patriarchal view of society. You likely see such distinctions because they were considered important enough, but this may not also be the case. Language change can be kind of odd and leave remnants of things that you would otherwise not expect (such as marked case in English, who vs whom, I vs Me).
As for the gender distinction in English, I think a lot of the masculine terms were originally gender neutral, and then people started adding feminine inflections to them. For instance, at least in my opinion as an English speaker, you could refer to both men and women as actors, but only women as actresses. In fact, from when and where I grew up, aside from feminist talks and the like, it has never been unusual to use "male" terms for both men and women, it's more like a gender neutral word, vs the feminine ones that are specifically only for women. English has also responded to the need for a gender neutral pronoun, as "they" has been adopted in the singular by most English speakers as a gender neutral third person pronoun. It isn't "officially" this yet, but it's definitely on it's way, if not already part of the language. My experience with non-binary individuals is that they either prefer "they" or they like your to switch between "he" or "she" depending on mood/context. There are others who may want some other form of pronoun, but I think for the most part this covers many of them. I've even seen some want "it" used, though "it" implies something is inanimate, and thus considered demeaning by many. Thus, we may eventually see "it" become an acceptable gender neutral animate pronoun in English, but I would speculate it won't because of "they" and it's popular usage.
Also, to add on to the discussion of gender, there are a few languages that you may be curious about. For instance, Japanese women used to have to use a different writing system than men (this is why there is both Katakana & Hiragana if I recall correctly). There are also aboriginal languages where the women have their own version of the language they have to speak (and I think one of them even has an additional form for speaking with mother in laws, but I'm not sure on that one).
Overall, a lot of the heavy focus on Gender from a grammatical perspective is clustered in the Indo-European languages, and particularly in the more popular European languages. This does not mean it doesn't occur elsewhere, just that it's heavily focused in a small sample of the world's languages that just happen to be some of the most spoken languages.
Also, and this is super important, I'm very rusty on all of this. But look into some linguistic textbooks on gender, or even investigate conlanging a bit. It's covered quite in depth, and you can even ask some questions on the conlanaging forums about how gender works in certain languages, why it's there, etc.
Language is extremely complex and beautiful, and why there are certainly effects from gender in language, their origins can be surprising when investigated and may actually serve a different purpose than what you imagine.
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