You're at school pickup. You mention watching the fights Saturday night. The look you get back is somewhere between confusion and concern. Welcome to being an MMA mom.
The elevator pitch: MMA is a sport with multiple martial arts disciplines, strict rules, weight classes, and referee stoppages. For the violence concern: MMA has a lower serious injury rate than football, hockey, and cheerleading.
If your daughter trains, lead with the benefits: problem-solving, discipline, confidence, fitness. The MMA community is welcoming once you're in it. You don't owe anyone an explanation for what you enjoy. Next time someone gives you that look at pickup, smile and say: you should come watch sometime.