Asking questions is one thing...but accusing him of lying is another.
A lot of people have accused him of lying - there's nothing wrong in asking him that question and his reaction to the accusations. You would be demanding the exact same thing if a Dem president was in the firing line.
Honestly, the President is not a wimp, he's handling these questions fine, and is leaving a better impression than if he was only having to answer softball questions from a sycophant.