While translating "homo" as "human" or "human being" is correct, it translates awkwardly into English. This just isn't something we say in English.
In the bad old days, the term "man" was used in a non-sex-specific way, and that's how "homo" would have been translated. But with that usage now radioactive, we're stuck with this clunky phrase.
Just speaking for myself--I never thought there was anything wrong with the generic use of "man", or the generic pronoun "he," etc. I continue not finding anything wrong with such practices in English.
I suppose "homo" can be translated as "person," for that matter, if it helps...
Well, that's more likely what an English-speaker would say, but I would say that as a translation of "homo," person isn't right. "Person" really isn't a synonym for "human." "Person" describes a state of being that isn't necessarily physical -- God is deemed to be a person, or even three in Christianity; and a corporation can be deemed to be a person as a function of law. There are some who argue that certain higher animals might have personhood -- not that I am agreeing, just citing this as an example.
And, I'm with you, I don't see anything wrong with "man" or "he/him/his" being used in the generic sense, but alas, that is deemed controversial today, if not archaic.
The generic use of "man" (to mean the species) in English confuses people. See, for example, Charles Rycroft, A Critical Dictionary of Psychoanalysis (New York: Basic Books, 1968): "The homo in homosexual derives from the Greek homos meaning 'same,' and not from the Latin homo, a 'man'; hence, homosexual can be applied to women as well as men." This is classic reference book, but the statement makes no sense since "homo" in Latin includes both women and men.
Notice that they're pointing out that homoios in Greek = the same, and that's the word used in the compound "homosexual" (compare heteros = another, used in "heterosexual").
Yes, homo in Latin includes both men and women, whether Charles Rycroft got the message or not.
And yet you sometimes see people inventing the term ad fēminam for an argument directed at a woman personally (rather than at her arguments or ideas), when ad hominem really should work for both men and women.
I think we in the US say this; I seem to remember some kiddie chant that we had, for teasing each other: "Johnny and Mary, sitting in a tree, k-i-s-s-i-n-g !" (with the relevant part there the "sitting in a tree"). That's going back quite a few decades; I don't know if the children still say that...