Now the question comes up is what are they going to do with the word “homo” which is Latin for ‘man’?
It's also Greek for "same".
-- a) From the Greek homos meaning same / the same, as in homosexuality (same-sex love), homogenous (uniform). (The opposite is hetero- from the Greek heteros meaning different from);
-- b) From the Latin homo, meaning human / human being (a member of the genus Homo), as in Homo sapiens, hominophobia, homicide.
That's why a lesbian is also a homosexual.