As far as I understand, the word ' homo' means 'man' in latin (as in homo sapiens which means "wise man" or "knowing man), ...

to tweak very slightly, it means 'mankind' or 'human'.

... but it means the word 'same' in Ancient Greek (apparently)

Whereas the Latin word is a noun, the Greek word is a prefix, as in homophone (two or more words that sound the same but have different meanings ie to, too and two) or homograph (two or more words that are spelled the same way but pronounced differently ie sow [plant seeds] and sow [a female pig]).

- but phobia comes from the Greek word Phobos which means irrational fear, ... its origin then has nothing really to do with hating (or even being afraid of) gay people.

The wikipedia article on homophobia highlights the fact that - whilst irrationality can come into play here - the term homophobia covers a multitude of 'sins', some of which have no irrationality in them at all.  Unfortunately, people like Martin like to use it as a term of abuse and almost emotional blackmail, making out that the irrationality element is the most important.  Some of the alternative terms listed in the article seem interesting - though not necessarily all that helpful.  For instance, the term 'homosexophobia' again highlights the idea of irrational fear which very few people actually feel.