Even diehard fans of Red Hood most certainly will attest to the matter. Ever since coming back from the dead, Jason Todd has been highly critical of Bruce Wayne's role as both an adopted father and crimefighter. However, readers have never been given much reason to take the antihero's words at face value until they were given a story to read from his point of view.
This is showcased in Red Hood and the Outlaws #25 by Scott Lobdell, Dexter Soy, Trevor Hairsine, Ryan Winn, Phil Hester, and Ande Parks, when Batman flings his own criticisms at Jason for trying to kill The Penguin. Their verbal disagreement quickly becomes a physical one when Batman turns his fury into fists against Jason's face. The disagreement becomes heartbreaking to read once Jason says, "You are a character. I’ve never seen you hit Joker that hard. And you hate him."
Suddenly, from a reader's perspective, years' worth of Jason's criticisms towards the head of the Bat Family have become clear. Batman is far more brutal to his family than he has ever been to any villain in his rogues' gallery. And the worst part is that Batman is harsh specifically because of the love he has for his sons.
Batman has an ongoing characteristic where he is needlessly harsh to those he considers friends, colleagues, or family–the latter of whom, as is seen in this issue, Batman's been borderline abusive and violent towards. Perhaps it is simply his love for his sons that makes him so harsh, as if his high expectations is what makes him increasingly critical. However, what makes this such a dark aspect to Batman's character that he needs to confront and change - besides the abuse, obviously - is when it is viewed in stark contrast to his rivals.
Since Batman has held his no-kill rule for so long, long before Jason Todd was ever even introduced as a Robin, it was hard for Red Hood's arguments to hold weight regarding whether Batman should be more vicious towards enemies. But Batman has proven time and time again just how forgiving and surprisingly patient he can be towards his worst enemies like The Joker, who still gets sent to Arkham Asylum in one piece after committing multiple mass murders. He's still violent, yes, but he has a father's patience in giving baddies second chances that he rarely affords to his own children. Meanwhile, the slightest of missteps in judgement that his sons make, like going a little too rough on someone like The Penguin, have proven practically unforgivable in the eyes of The Bat.
No one is saying that Batman should reconsider his kill rule or that he should be harsher on his enemies, but what he should reconsider is why he is so harsh on the boys he sees as his own flesh and blood. He is much harsher on Red Hood in comparison to others who've taken up the Robin mantle. These have been common criticisms that Jason Todd's Red Hood has flung at Batman in the past, but all it took was one brutal line to expose the real brutality behind Bruce Wayne.