Its not the name itself really
Its that he's lying to people implying that he's teaching a defined system when its more of his own person mixture of martial arts. If he marketed it as MMA I'd be fine with it, but when he tries to exploit the ignorance of the unknowing by attempting to brand it as a defined traditional martial art.
On a side note, I just noticed this -
Wu'Chi Kwon Do literally means 'Fist of Nothingness'. It is a term used by this school to describe the type of techniques taught. However, what is being taught is a Freestyle Karate. Freestyle Karate is a recognised form of martial arts. It is very disciplined like traditional karate, but allows for a greater range of movements.
which clears up quite a bit. Whoops.
How's he lying? Anyone can make up a system. Watch this:
White Belt: Intro Movements and Warm up
Yellow Belt: Basic Form 1 (the one I like from kung fu), Jab, Cross, Hook, Front Kick, Self Defense 1-8
Orange Belt: Basic Form 2 (The one from TKD class that uses front kick), Upper Cut, Overhand Right, Round House, Step Sparring, Light Contact Sparring
Blue Belt: Basic Form 3 (The one I just made up where you repeat sparring steps 2,3 and a self defense move 4 times), hard karate blocks, BJJ escapes and transitions
Green Belt: Basic Form 4 (The second Kung Fu form), sticky hands trapping, full contact sparring, arm bar, rear naked choke, single leg, double leg, americana, hook and side kick.
Black Belt: Do it all better.
There. That's a system. A defined system. If I've done martial arts for 6 years, that's long enough to make a defined computer programming protocol, or a triage protocol, or a fire hose hookup protocol. It's enough time to make a defined training protocol. Anyone running a McDojo is free to use what I just wrote as a template, free of charge. Its called "Summer Striker Kwon Do." Search it on line. It was invented by me in 2013.
What matters is that the head instructor is knowledgeable, believes in what he is doing, and teaches to the best of his abilities. People go to him because they are getting what they want. Branding and marketing is not a sin. It is a sacrament. If he can make money teaching, than he can teach and train full time, making him better than he would be if he blundered through it acting like the spirit of martial arts is dead in him because he isn't parroting a tradition from someone else's culture that he doesn't care about.
Anyone with a library or an internet can look to see if you made up the name of the martial art. He isn't even lying about that anyway. Like I said, Branding is important. Capital B important. People can empirically tell if his teaching is good by finding martial artists or MMA people and sparring with them. If they get beat up, they should figure out why. I did. I left my old instructor when I found a more effective one. If people are too stupid to research the history of a martial art if they care about the history of the martial art, don't care how their training stacks up to other people by never checking, and can't tell that their instructor lacks the self objectivity he needs to tell if he should be teaching, all of that it their fault. In this day and age, there is no excuse.