The parents never hit their child (back), by the way, only she may hit them if she asks, and is allowed to.

Two excerpts that explain the underlying philosophy:

In the world, Nic points out, women are largely on the receiving end of violence, and in his family that was contrasted with his mom, who would teach the kids judo and jujitsu techniques. His aunt was a national judo champion, and the best judoka in the family. People would come to spar with the family, and they would be paired with his aunt, who is 5-foot-4 on a good day. He grew up seeing pictures of her throwing 200-pound men, their heels flying in the air. Then he would see other people’s families, in which violence was just framed as a negative, end of story.

Margo wants some of Nic’s female relatives’ confidence for our daughter—whether or not she wants to be a martial artist, Margo wants her to be physically prepared for life. Margo has felt so unprepared physically for so many scenarios she’s found herself in, starting with being a young woman in New York City, getting grabbed and groped and followed home and jerked off to on the subway. She wonders how she could have responded differently to all those incidents if she’d had a practice of physical mastery that wasn’t dependent on size or brute strength.

After a lifetime of seeing those dynamics, Nic wants the same thing for his children that he was given: the power to protect themselves and the people around them, and the knowledge to be able to know what does and doesn’t warrant a physical reaction. “I give them a space in the home to practice learning those parts of themselves,” he says, “so if they are in a situation, they are not in that space for the first time.”

“I just want to cultivate children who can protect themselves.”

I like that it involved a girl in this case, but it could also allow boys to still fight eachother as a form of consensual play, and accepting "no" for an answer. Just saying "all violence is bad" can lead to problems down the line when they can no longer control themselves and have zero experience.