I have two small children of my own, so I know the behaviour :-) None of what you say negates the fact that at the point in time that the child says that they hate the thing they hate, they really do. As I say, hatred is a subjective emotion not necessarily informed by objective reason.
I'm not denying the emotion or the words. I'm just saying they're wrong about what they hate, because what they hate isn't what they're saying.
If I say I hate you and your lying ways, the hate is real whether or not you've lied. But if you've never lied, then I'm not actually hating anything real, just my false idea of a real thing. I literally don't know what I'm talking about.
And now I think we've demonstrated why people hate philosophers.