The difference comes from "let" and "have"'s the relationship between two people. Have is usually said from a more commanding or dominant person. I.e. Kid: "You're a stupid poop" Teacher: I will not have you speak like that. The "have" implies the control or power the teacher has over the kid. "Let" is used more for equals. Friend: I'm fat and stupid. You: I will not let you say that. You feel equal to your friend and you want to be a little nice about that. If you wanted to be more commanding, you could use the "have" example. That implies you feel more strongly about it.