You are both right. It all depends on the tone and context in which it is said. The example that you gave illustrates when you are certain that something will happen. What your teacher is talking about is when it is said to be ironic or sarcastic. For example, if someone says "I can speak 10 languages" and you don't believe them, you could say "yeah, I bet you can(!)". In this context, is the same as saying "yeah right!"

I think it is more about showing confidence than certainty. Like you are confident enough that your favorite sports team will win so you are willing to bet money on it. But since you can't actually know for sure nor you can see in future that your team will win it isn't confidence based on certainty. I think in situation like "I bet you can't do a flip" it still applies. You are confident in the lack of your friend's skills. But overall I don't think it is uncertainty either, no one would bet on things they know they wouldn't win.