This was a brand new phrase to me and I quite like it. A similar phrase is ‘I don’t have a stake in this game’ which is self-explanatory.
If you don’t have a dog of yours in a dog fight or a horse in a horse race and are not betting on either one, you have no interest in taking sides. The expression is sometimes used to emphasize that the speaker is disinterested though he or she may be offering advice or commentary on the subject in question. This claimed lack of any ulterior motive supposedly enhances the reliability of the advice or comments offered.
It may sound like ‘an old Southern expression,’ but there is little evidence of it being old or necessarily of Southern origin. Google suggests that it is a recent saying, along the same lines as calling someone “all [cowboy] hat and no cattle.”
The term, now that I’m looking for it, seems popular, though dogfighting is illegal in the U.S. and in Britain. It’s common in Mexico, and in Texas as well, although conducted clandestinely there. Dog racing still goes on in Britain, and the phrase can easily be switched to ‘I don’t have a dog in this race.’
Another slant is that ‘dogfight’ is the metaphor used for the combat between two fighter planes, as it has been since World War I.
A couple of weeks ago, I mentioned that I submitted my short story Grand Champion to a Canadian anthology of humor. I received a rejection a couple of days ago. So I no longer have a dog in that fight!