CMV: the elimination of genderless "man" is paradoxical.

I am a non-native speaker. I recently found that this phenomenon is very hard to understand for me. I don't want to debate over the necessity of adopting inclusive language. I understand the need for native speakers to use gender-neutral language to promote equality. But it really brought me a lot of confusion.

I learnt that the word "man" is for both male human and general human beings in my primary school. However, I now find that the genderless use seems outdated. The use of genderless man is inappropriate in modern English, so "fireman," "chairman," "freshman," and "unmanned" all need to be changed to neutral words. But in this way, the "man" in "woman" is also genderless (it is from Middle English mann) and should also be replaced by some other words like "female human," newly coined "woperson," or the resurrected Middle English word "wif". It is inconsistent. (originally "It seems like a paradox and makes no sense logically" before OP editing it.)

I have searched on the internet cannot find some theory to explain this phenomenon properly. If "woman" has been widely used and cannot be changed, words like "fireman", "freshman" were also widely used, why should changes be made? If the public has strong feelings for "woman", is it possible that firefighters also have feelings for the word "fireman", and college students will also miss their life in freshman year? Is this ignoring the emotions of these people?

Is it a kind of compromise? Or just because the etymology origin of "woman" is less obvious than "chairman" for native speakers? If it retained the equivalent form "wifeman" of Middle English word "wifmann", would it be considered non-inclusive and get changed?

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Actually, the coexistence of male-specific "man" and "woman" that has "man" as a compound gives me a strong feeling of androcentrism and objectification. I am always very uncomfortable when using them, so I tend to use "males" and "females".

I think it is the easiest solution to use the ungendered man, and a male word like resurrected "weaponedman" (or simplified "wepman", from Middle English wæpnedmann) or newly coined "maleman". In this way we could keep both "woman" and other words with the ungendered "man" as a compound, we just changed one word (the male word). Compared with the current solution in which almost all other words with genderless man are changed, it could minimize the impact.

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Note: I am willing to change my view because I understand that I may have ignored some society and history knowledge of English countries due to lack of literatures (or just I did not find them). So please provide more information and views from native English speakers or non-native speakers from diversified cultural backgrounds to help me understand it.