Part of it, I think, is that he may honestly believe he's warning her. After all, he is giving her a clue to Batman's ID. It's a token of good will. He got fucked over by Bruce, and he thinks that the same is going to happen to Mia. By letting her know he's the same as her, he's basically letting her know that when things go wrong with Green Arrow, he could be her ally.
And there's the Bruce factor. He's also doing all this because he wants Bruce to know that he knows things, he can have an impact on Bruce's friends, Bruce's people.