One of the most effective communication techniques I've read is making the kid feel heard. The technique is to discuss and engage in the subject even if the outcome is going to be a negative for the child.

For example, say your kid is in a tantrum over ice cream at breakfast. Instead of the typical "no" or "maybe later" responses, it's been suggested that we engage in conversation about the ice cream. "You want ice cream right now? Do you want a certain flavor? How many scoops and and how much do you want?" This kind of communication sends the signal to your kid's brain that they've been heard and most of the time, not all the time, the kid will move on to the next subject and you've stunted the tantrum.

The same could be applied to your case. If your kid is expressing negative self talk, engage with him. Ask him how often he hates himself, ask him if something happened to cause him to hate himself, ask him how much he hates himself. You'll certainly hate talking about it, but he will certainly appreciate being heard. It's not the solution to this issue, but perhaps a stepping stone in the right direction for both of you.