While this is true, I think you're forgetting about all of the ways men could be injured that don't involve actively protecting women.

Need to muscle some livestock? Probably mans job.

Need to cut trees? Probably mans job.

Need to stalk wild game through the forest? Probably mans job.

Need to lift heavy things that could injure you? Probably mans job.

A teenager being too aggressive and overdoing some activity? Probably a man.

It's not hard to see all the ways men could be injured by being men, that doesn't involve protecting women from predators.