One of my local Twitter contacts is rueing the moment they decided to step in to break up a catfight. Doing that is like having a wrestling match with a roll of barbed wire. Both cats went for either forearm, and wounds inflicted by both claws and teeth of a cat tend to get very nastily infected.
I recall having a similar experience some 25 years ago, when my sister had left her two kitties at my parents' house for a week or so. Bear in mind that at the time we had our own cat, an un-neutered tomcat called Thomas (above), in the house. Territorial was the name of his game, so when someone left a door open I found myself with Thomas to the right and the guestcat (whose name I cannot reveal on here) to the left. Thomas went into fighting mode, ears back, crouching into attack pose, whilst the guestcat ambled in, tail up and almost saying "C'mon, let's have it out then". I stepped in and put out a hand to push each cat away. Thomas thought the other cat had jumped out at him and lunged into my forearm - only to immediately recognise his mistake. He disappeared. I bundled the other cat behind the door where he should have been all along. I found Thomas sitting in the window of the nearby sitting room and he rubbed his head against my hand, almost as if to say: "Sorry about that, boss, didn't realise it was you. You could have fooled me it was another effing cat". I had a deep wound of one of his claws, but it was only a fleshwound, nothing serious.
Thomas has made me ill on one occasion, but again, not his fault. He tended to be infested with fleas, and one day I was given the job of powdering the cat. Neither of us liked it, and I used rather too much powder. Thomas looked white, rather than his normal black and within a few hours I started to feel feverish and quite unwell. Anyone who has ever dipped sheep with the old organo-phosphate sheepdips will know the feeling.