I was wondering if I could do this: The real question is: why do you hate her? If I can't do that, how can I put a question in a statement?
The way you have it written could be grammatically correct, but the colon in this situation gives it a cheesy-dramatic-pause-Law-and-Order-dialogue kind of effect. If you'd like to have the reader take you seriously on this piece of dialogue, the comma in Cogito's post would be the way to go. At least I would prefer that if I were reading it, and I'm a fan of colons & semicolons.
