“Bruce doesn’t call himself the batkids dad”
Bruce will not insult his children’s intellect by assuming they were not of sound mind or did not mean what they said when they tell him he is their dad. This is genuinely the one thing for Bruce that is a no-take-backsies
They are not siblings, they do not have to interact with each other- he only cares that they are civil and polite- but they are his kids.
This man literally says it himself “they may not be brothers but they’re both my sons.”
Yes, he is a deeply insecure man who worries about his worth in his kids lives. But he never doubts that they in fact view him as their father. They tell him once that he is a father figure/father/dad-shaped and they will never be able to recant that.
He is their dad, those are his kids, end of discussion no take backs.