Assuming a male speaker is referring to an ex-partner, which of the following is more correct?
- She left me for another woman
- She left me for a woman
The phrase She left me for another man has always made sense to me because the omission of another would suggest that she did not have a man before she left (a subtle self-deprecation on the part of the speaker). Similarly, a female speaker would say He left me for another woman.
Should the rules change when the new partner is of the same gender?
Contrary to the other answers, I think "she left me for another woman" is perfectly fine, and does not imply anything about her earlier relationships (other than with the speaker). It is true that in a sentence like "she left me for another man", the another means other than myself, a meaning which does not apply (since the speaker is male) to "she left me for another woman". But here, "another" can mean other than herself. For instance, in a sentence like "Shane was pleased to see another Australian in Cairo", the "another" only means "other than himself", and does not imply that he'd seen other Australians before. Similarly, "she left me for another woman" does not necessarily imply that she'd been with a woman before, I think.
That said, I think "she left me for a woman" is fine, too. It does not have the problem you mentioned that "she left me for a man" would have (self-deprecation on part of the male speaker), and if some people are going to (mis?)interpret "another woman" as meaning that there was already another "another woman", then it's probably best to avoid "another".
Assuming a male speaker,
She left me for another woman
implies she left the man for a woman, having already been with women in the past. The “another” refers to the fact that there already are women in the woman’s past, and the one she left the man for is one more.
She left me for a woman
implies she left the man for a woman, and this is the first time she has been with a woman, as far as the speaker knows.
Weird sample sentence, but anyway.
Considering that "another" in this context means "different or distinct", it seems appropriate to use simply "She left me for a woman".
"another" would seem to indicate that there is some woman in the equation that she is no longer with.
In a similar example, you could say.
"My wife bought a purse. She didn't like it, so she returned it and bought another [purse]."
But:
"My wife bought a purse. She didn't like it, so she returned it and bought a belt."
The only reason to insert "another" in the second sentence is if you're implying that she already has a belt currently (and that this adds to the collection). In this context, "another" would mean "being one more or more of the same".
Definitions from Dictionary.com
If you say
She left me for a woman.
it would imply that she had given up on you and on men in general.
If you say
She left me for another woman.
it implies that you think of yourself as a woman, or she does (or did).
If neither of the above is true, it is correct to say
She left me for another man.
The idea here is that "She left me [to go with] another man."
The for in this case is used in its sense of "assigning" one thing to another.
"She left me for a woman" is more correct but "She left me for another woman" has a poetic and humorous quality, being a play on a standard form.
:)