Look, no one’s saying it’s impossible for a trained woman to beat a man. When we start talking about individuals, all bets are off. Some men will simply cower and fold at the first physical contact, and allow themselves to be beaten mercilessly. There are obvious grades of ‘couch potato’, too. As well as obvious differences in strength and talent level among women.
Given the parameters of the question, however, we are of necessity talking about generalities. I take ‘a trained female martial artist’ to mean a composite of all the women out there who have achieved a black belt in Karate. Not the most ultimatest, meanest, killingest woman on the face of the planet. And by ‘couch potato’, I assume we’re talking about your average guy who goes to work, comes home and sits on the couch and watches TV, and is carrying around a decent-sized spare tire. Not a slovenly blob of meat who can’t get off the couch.
So given those composite characters, I happen to think the man would win most of the time. I know several female black belts, and not one of them has a ‘killer instinct’. They’re not mean people. They may never have had serious physical contact in their lives, even in training. They also may have an over-inflated sense of how well they might do against a man, because during their training the men may have gone easier on them and they don’t know it. I know I sure did - there was no way I was going to open up a full power roundhouse kick on a 110 lb woman in training like I would on a man of my size, so when I sparred with women I held a lot back. So did everyone else.
My experience comes from actually sparring with women, and being a training partner holding heavy bags and kicking and punching targets. I may have held back, but they generally didn’t. And in my style, we fought full-contact to the body and semi-contact to the head. So I’ve been hit many, many times by women of all levels of training, with everything they could muster. And believe me, there is simply no comparison in strength and power to what a man can deliver.
So for a woman to beat the man, she has to have big edges in other areas, which I mentioned. Excellent grappling skills might do it if she gets a chance to use a submission hold and has the strength to maintain it. A vast difference in desire or ferocity would help close the gap. If she’s really fighting for her life, then going for the eyes would be a great playing field leveler.
But in general, what’s going to happen is that the man will simply overpower her. I’ve seen women fight men for real before - usually at crazy parties where someone throws a fit and goes berzerk on the boyfriend or someone else. The man usually ends it by simply swarming her, pinning her arms and legs down, and telling her to calm down. There’s never any question as to who might win the confrontation. He might even get hit a few times. A good solid punch might even leave a mark for a few days. That’s about it.