why might arthur behave in such a casualmanner after witnessings such a scene?

King Arthur is exactly that, a King. The Green Night comes traipsing into Arthur’s castle. Its Christmas dinner and Arthur is with all his knight buddies. I'm sure Arthur was shocked as everybody but a king can hardly show it. Arthur is like head of the Knights of the Round Table! I think Arthur was pretty relieved when Gowan said the challenge was insulting to a king and volunteered himself.

To be sure Arthur wan't a total whimp though.He does challange the Green Kinight after being mocked for about ten minutes! Fortnatey Gawain moves in to take the challange.