Just as Bruce Wayne (Batman) will not use a gun - he would NEVER do anything to harm a child that age.
What is “that age”? About the age that Bruce was when he saw his parents gunned down.
So why does he want to see a child the same age as he was taking on armed men and beating them?
To torture himself that he could have/should have done SOMETHING - even as a young boy - to prevent his parents being killed.
He wants to prove that a “Boy Wonder” could take on and win against an armed man. To torture himself that he did nothing.
If anyone has a better take on the subject than this I have yet to hear it.
Being cynical and jaded, I always assumed Batman had to have a Robin for copyright/marketing purposes.
But seriously, your take is a fresh one and, quite honestly, brilliant. One that writers and moviemakers have, to my knowledge, missed.
There have also been periods when the comic went back to fundamentals and Batman as the solo "Dark Knight" -- no Robin. Actually, Robin came along pretty early, but purists didn't really like him, especially after the campy 1960s television show.
The thing to understand is that most of these comic book characters had sidekicks, woman or boy or girl auxiliaries or assistants, or younger selves featured in stories or in their own comic book. So there was Superboy and Supergirl, Kid Flash, etc. Green Lantern and Green Arrow and Acquaman also had sidekicks. They helped to generate stories and sell comics and gave a "family feel" to comics at a time when that was thought to be a good thing.