Answer:
Hi! I'm afraid your question is incomplete, you don't mention which text are you talking about, nor even the author. Anyways, I did a little research on the Internet and I found out that this tasks refers to a text called Sir Gawain and The Green Knight, written by the so called Pearl-Poet. I'll try to give a precise answer with the information I found.
I think that Sir Gawain flinched when the Green Knight brought his axe down because he was afraid he could die, but the Green Knight did not because he knew he wasn't going to die.
Step-by-step explanation:
The reason for Gawain's behaviour was his fear; he knew he could die if he was touched by the axe. On the other hand, the Green Knight knew he couldn't, so he was fearless. The Green Knight was testing Gawain, he didn't care about the axe because he knew it couldn't hurt him.