Suppose, just for a second, that Dick Grayson, teenage acrobat, is orphaned by a killer. Suppose, further, that the circus life is all Dick has ever known. He has friends there, and it's rough life, it involves a lot of travel and a lot of hard work, and he has never had a real home outside of a train car or a truck or bus or whatever they use these days. His family are acrobats. He has already been putting his life on the line every day for as long as he has been physically able to perform on the trapeze.
When his parents are gone, his usefulness to the circus is gone as well. His friends care for him and maybe he tags along with them for a while but he has no real job in the circus any longer.
Now I need you to consider. Dick is not a legal resident of ANY city. He lives on the road. He is a carnie, basically a drifter, and he is a teenager.
Allow me to remind you what it is like to be a teenage boy. You are moody. You are, sometimes, a git, and for no reason other than you woke up feeling that way that day. It's a hormonal thing. It happens.
Furthermore, in case you have never experienced the death of a loved one, let me explain to you that it is usually accompanied by a bit of anger and helplessness. And because Dick was present when it happened, he is also going to feel some survivor's guilt.
Now then. As we have established, Dick is a carnie. Therefore, he is used to having to solve his own problems. He's angry at the guy who killed his parents? No problem, the solution is to go kill the guy. He feels helpless for the first time in his life? The solution is to go do something proactive, like, let's say, hunt down his parents' killer. He feels survivor's guilt? Risking his life to avenge his parents deaths would seem to address this concern as well. Dick is going to go out into the night and try to find his parents' murderer. And he isn't going to need Batman's help to do it.
Hell, at this point he doesn't even KNOW Batman.
Now, there is no social services person coming for Dick, because he is not a legal resident of anyplace. There is nobody looking to adopt this kid. And then Bruce Wayne shows up and offers to give him a home. I think Dick is going to resist this, but he's not an adult and the people at the Circus are going to think that Bruce can give Dick a more normal life than they can.
Dick just wants to avenge his parents' deaths. And Bruce... Bruce wants to protect Dick. Bruce wants to save him. Not to make him into his sidekick. Batman works alone. Bruce wants to PROTECT THE KID.
But he can't stop Dick from trying to find his parents' murderer. He just can't. It would be a full-time job and Bruce already ha a full-time job wearing a cape. He wants to protect the innocent and among them is Dick, but he can't protect Dick AND protect everybody else at the same time. And Dick doesn't want protection. Dick is not helpless, and he is not content to stay home or go to school or do any of those things.
Bruce knows the anger that drives Dick. He wants to take that anger away from Dick, but he can't, and Dick is actually SAFER if he is where Batman can keep an eye on him; Dick is SAFER if he has been taught Keysi Fighting Method; Dick is SAFER if he has body armor and tools. Because make no mistake about it: Dick is GOING TO SEEK VENGEANCE regardless of whether Bruce helps him or not. Bruce's guidance could be the difference between a dead child and a living one. (Bruce's guidance being the force that keeps him alive, of course).
So, it IS helping him. Because without Bruce's training, Dick is going to get himself killed. And there's NOT A DAMN THING ANYBODY CAN DO ABOUT THAT.
Dick never HAD a normal life. He had a happy life with the circus, but it sure as hell wasn't NORMAL. That's kind of the point, isn't it? Dick never had a normal life. He didn't grow up in suburbia playing stickball with Billy and Tim. He grew up shoveling elephant dung and listening to drunken old clowns telling dirty jokes. He grew up with bearded ladies and triple-breasted ****es, he grew up a sort of star in his own little world, learning the family trade and learning to do it right so that he would not die attempting it.
If Robin chose to be a warrior, Batman can't make him take back that choice. And the world needs heroes. A properly trained soldier is always preferable, and less a danger to himself, than one who has no idea what he is doing.