Oh, I see what you mean. Thank you for the clarification.
But what you are referring to is more about meaning rather than truth. Something is not "more true" because it's more meaningful. This is a bit a dangerous area to get into, too, because one could believe something to be true because it feels meaningful. So, when you say that when you hate someone you are hating yourself, that might feel like it has a "deep truth" because it feels deep and meaningful. But that doesn't necessarily make it true.
Jordan Peterson has talked about this. He seems to think it's worth believing things if they have meaning, and if they benefit us in some way, even if they might not be true. I'm not sure I agree with that. I'd rather know what's actually true.
It could actually be dangerous to tell someone that if they hate someone else then they are really hating themselves. It could lead to unnecessary self-hatred. In fact, this is what gaslighting bullies do. They turn a problem around and make out that it's the victim's own fault.