Archimedes tried to help Wart the entire movie,he's one of the heroes.He argue with Merlin constantly but love his master and helped in teach and guide Wart (Also he have the best laugh in Disney history,tied with ED from TLK hahaha LOL)Â
I think that Archimedes said that he could eat the pike to not admit that he wanted to save Arthur (because in the previous scene he was angry with the two). The owl is kind,caring and helpful but he's grumpy,sensible and sarcastic too. I think that much people have this traits of this (sometimes) highly educated owl.