The argument I responded to originally was that Robin adds "unnecessary light" to Batman, as Batman should be "dark." This is a naive argument, as while Batman may be dark, the theme of Batman comics has always ben conquering the dark. The sacrifice Bruce Wayne has always believed necessary to do his job was that he could have no personal life, no happiness for himself. He has always believed, deep down, that it was an either/or chose: either he has a life, or he has the mission. More importantly, he has always wondered if it meant the sacrifice of his humanity--that he would have to be ruled by his darker nature, and even use the tools of evil to defeat it. Violence, anger, guilt. The purpose Robin serves, more than anything, is to demonstrate to Bruce that it doesn't have to be that way. Dick Grayson is the version of Bruce Wayne that was able to find balance, and still be dedicated to the mission without sacrificing his own humanity. Dick is, for all intents and purposes, a happy, well-adjusted, healthy individual--everything Bruce doesn't believe he can be.
Batman needs Dick, because nobody else can demonstrate this quality. Nobody else lives the life Batman does--nobody except Dick Grayson. Nobody else has come from that same place of tragedy to take on that same mission. Accordingly, Dick is the only person who can show Bruce that the life doesn't have to swallow him up. Dick is the person that Bruce wants to be, even if he could never admit it..
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In a way, the struggle isn't purely "Can I, Bruce Wayne, defeat evil without losing myself," because if the defeat of evil means the loss of his own humanity, he'd pay that price readily. The struggle is "Can the human race defeat evil without losing itself." Every time Bruce looks in a mirror, he sees that the answer is probably no. But when he looks at Dick, he sees the answer is probably yes, because Dick has already done it. Dick never gave himself over to the dark the way Bruce did; he's always been able to keep that balance without sacrificing the mission. Dick gives Bruce hope that humanity can overcome evil without becoming it. If everyone was like Bruce Wayne, evil would be gone, but we wouldn't be human any longer. If everybody was like Dick Grayson, evil would be gone and we'd still be human. And yes, somewhere Bruce also sees hope for himself in Dick, not just for humanity.