Every good superhero knows they need to keep their identity a secret if they want to protect the ones they love.
It should come as no surprise then that Batman (the smartest superhero in the DC Universe) is smart enough to cover his face and mask his voice when he's out protecting Gotham. How terrible would it be if the Joker or Two-Face knew his identity? It would be devastating. Wayne estate would be on fire with in a matter of hours.
Which is exactly why your kid is demanding a mask. They're trying to keep you safe by keeping their identity a secret. Just let them don this Child Affordable Batman Mask and they can speed off to fight crime without endangering their family or home. Or, you know, run around the living room screaming something about being the "Dark Knight." Either way, the mask is a must.