The widely accepted meaning of this character is that the characters for "female" (女) and "child" (子) were put together to form a compound because it was good for a woman to have a child. Similarly, it has been proposed that the compound originally refers to the mutual affection between the mother and child, which then extended to mean "good". These theories are supported by the smaller 子 found in some oracle bones and bronze inscriptions.
However, broader interpretations of the second character 子 could lead to other theories. 子 could also mean "son", so it may have meant two children, a boy and a girl next to each other, which is a good fortune to have a boy and a girl. 子 could also mean "man", so it may have referred to the love between a man and a woman, which is good. Duan Yucai, in his annotated version of Shuowen, interpreted it as originally referring to the beauty of 女子 (nǚzǐ, “woman”). Lastly, it could mean that the "attitude" of a girl was considered good.
The two pronunciations are cognate – pronunciation 2 is the *-s suffixed form, or exoactive/putative of pronunciation 1, literally "to consider good".
This word has been compared with Proto-Sino-Tibetan*hu (“to raise; to rear; to nourish”): Proto-Lolo-Burmese *hu3, Abor-Miri u, Qiang (Mawo) χu, which is only attested in a limited number of languages. If this is correct, it may be related to 畜 (OC *l̥ʰuɡs, *l̥ʰuɡ, *hluɡ, “to raise; to rear; domesticated animal”). Alternatively, compare Tibetanམཁོ (mkho, “necessary, important”).
Cognate with Central Baihux (“good”), which may be a loanword from Chinese.