6 y/o son being mean to others

I feel stuck with my model and need help please. I can’t really see how I can change my thoughts here.

C: My 6-year-old boy said to other boy when passing: “You’re ugly.” (Not the first time he said mean things to others)
T: I can’t believe he said this. This is not how I want my kids to behave. This is not what I teach them.
F: Shame
A: I get angry. I ask him why he said this. I ask myself what I did wrong that he is so mean. I keep asking him what he was thinking. I explain how hurtful this is to others. I ask him how he would feel if someone said this to him. As he does’t respond much and does’t show any kind of understanding, I keep going. I wonder what I can do to make sure he is treating others with respect. I worry he will experience rejection if he treats others like this. We move on embarrassed as the boy’s family is outraged.
R: I’m afraid he will say mean things to others again.

Thank you so much!