You only hate in others what you hate in yourself.

In some extreme examples it is more like "what you would hate in yourself" or "very nearly what you hate in yourself".

If you use your irritation, anger, and strong negative reaction ("hate" is a strong word) as beacons of light they will teach you about yourself.

Sort of like lighthouses that you should go toward instead of away from.

Facing your fears and looking your hatred in the face can show you a lot about yourself.