Expression is used to politely refute or disagree with the other person's statement. Used in response to a compliment to show modesty. Can also be used lightly criticize or scold someone.
Example
잘하기는요. 저보다잘하는사람이많아요.
I'm not that good. There are many people who are better than me.
2.
Contrast
Used to contrast the current situation with a different situation. The speaker acknowledge the first clause but want to express a difference stance or view. Only the 기는 form is valid in this case.
Example
우리아이가시끄럽게하기는해도말썽을부리지는않아. 그러니까걱정하지마.
Even though my child can be noisy, they don't cause trouble. So don't worry.