The reading of 大人
The reading of the word 大人 is quite irregular - おとな.
I wonder, is it related to the words 男（おとこ）and 女（おんな）?
おとこ + おんな = おとな ?
Men + women = adults. It makes sense to me, but please forgive me if my guess is incorrect.

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Hi!
There are combinations of Kanji that aren't necessarily read as one would expect. These are called (Jukujikun 熟字訓) and there are many of them. So they simply need to be memorized.
Other examples:
 昨日(きのう) "yesterday"
土産(みやげ) "souvenir"
二十歳(はたち) "20 years old"

Answer

Your guess is interesting but OTONA is a very old word, which has been used since more than 1000 years before.

OTO of OTONA is supposed to come from OTOTOKESHI(偉し）, meaning "large", "giant".

Its original meaning is "a person who finished the ritual to be regarded as an adult".

おとなしい has the same root  as 大人