What about Homo sapiens? Does he object to this word too?
OK, so, Homo in "Homo sapiens" means "wise man" in Latin, Homo =man and sapiens = wise (edit: wise in this case is taken more in the sense of intelligent, able to understand, obviously there is a difference between wisdom and intelligence). The "homo" in homophone, and homosexual, does not come from Latin, it comes from Greek. The word in Greek is:
ὁμός
The first letter of that word is an omicron, roughly an O, except that in ancient Greek, many words that began with vowels had what is called a "rough breathing". A word with a rough breathing was pronounced with an H sound. Thus a word starting with Alpha (A) and a rough breathing would be pronounced "Ha". Transliterated to English to capture the sound, this word would be written "homoss". Appended to another word as a prefix, the sigma (equivalent to S) would be dropped and you just get Homo.
As to the meaning of the word itself, this Greek word meant "same". Thus homosexual does not mean "mansexual", it means "samesexual".
Just in case anyone wondered if homo sapiens and homosexual were related as words, they are not.