Because it's the way you see something doesn't make it so.
Thanks for your permission to be offended, but I don't tend to take deep or personal offense to things that are simply wrong and come out of ignorance, like an elderly person who I know isn't really bigoted referring to all Asian people as "Chinamen". Here, that you can't be bothered to look at, consider or understand your potential misuse of a turn of phrase when it's pointed out, that's a you problem, not a me problem.
Not that you would seem to care, what I do find offensive is when people believe it's their right to decide what should or shouldn't be offensive to someone else, especially when an offense has been pointed out and explained to them. But in some of life's situations, we can make up our own definitions for terms and generally do whatever we wish. This is one of those for you, and I don't doubt that among minor occurrences, you consider this a minor, minor occurrence.
Hmm, but just maybe if you find yourself about to refer to catfighting in the future, because of this minor occurrence, you'll pause, remember that even though you feel you got away with it, saying that in your view catfighting can refer to anyone without regard to sex was something you stubbornly made up to preserve your ability to feel right, and not use it.
And "sniping" is one of the possible gender-neutral alternatives for petty, backbiting type disputes between people.