Indeed, Reep is excessively honorable, but that's one thing that makes him so cool. I think it was a great juxtaposition, putting him and Eustace alongside each other, because they were such total opposites early on: Eustace was practical, materialistic, cowardly, and overly "modern". Reep was visionary, faithful, fearless, and devoted to the ancient code of chivalry.
And, of course, if you don't buy that, then at least you can still enjoy the scene where Eustace makes the mistake of trying to grab Reep by the tail and twirl him around. Reep promptly whips out his sword (you have to question Eustace's judgment, picking a fight with an armed adversary when he's unarmed) and pokes him in the hand, making him drop his tail, then:
REEPICHEEP (brandishing his sword): "Why do you not draw your own sword, poltroon? Draw and fight, or I'll beat you black and blue with the flat!"
EUSTACE: "I haven't got one. I'm a pacifist, I don't believe in fighting."
REEPICHEEP (very sternly): "Do I understand that you do not intend to give me satisfaction?"
EUSTACE (nursing his wounded hand): "I don't know what you mean. All I know is that if you can't take a joke, I shan't bother my head about you."
REEPICHEEP (beating Eustace with the flat of his sword): "Then take that..." *WHAP!* "And that..." *WHAP!* "To teach you manners..." *WHAP!* "And the respect due to a knight..." *WHAP!* "And a Mouse..." *WHAP!* "And a mouse's tail..." *WHAP!*