I don't have any advice what to do, but perhaps how to think about it.

I've read, and I believe, that this kind of outburst is actually the child talking about themselves.

When they say "I hate you!" it is more often than not telling you that your child is unhappy with his/herself. Thinking back on my own teenager-hood, this holds true for me.

These are the things I tell myself. It helps me keep on an even keel.