I’ve been thinking about this question. It’s a good one.
T'Challa would have to hit Erik where it hurts most. And that would be not being actually sensitive to all Erik has been through in his life. From his mom being away in jail, his dad’s murder, growing up quickly, and wanting to avenge his dad’s death. T'Challa empathized with him, but if it all turned out to be a lie just to get Erik to not destroy Wakanda, he’d do more than hate T'Challa, he would want to kill him all over again.