Here's the thing. No other martial arts school is my competition. I primarily teach teens and adults, so fitness classes are my competition. Extended work hours are my competition. Mountains of homework and college prep are my competition. If you teach kids, then little league is your competition. Soccer, football, dance, gymnastics, even video games. That is your competition.
Here's a great example. For those who don't know, I currently rent space from a Taekwondo school to teach my classes. I don't have anything to do with their program, but I do try to support them (considering if they close, I'm out of a space). Yesterday they attended a "Meet the Teacher" event at the local elementary school, as did three other local schools. While you can definitely sense the tension in the room between the school owners, everyone got their fair share of leads and sign ups. It's a school with 1,400 students currently enrolled. There's enough for everyone, without the need to belittle or bash the other schools.