@courtenay: Got it! Just thought it would be a nice nickname considering that most people with the name (courtney) have a nickname of  "Court" 

Posted by: @courtenay

And then if, as you suggest, Reepicheep's only fear was not being brave enough, losing his honor in front of others, maybe the narrative could have added that this one fear was as real to Reepicheep as the humans' fears of their own nightmares

So to sum it up, the Mouse's pride of himself gave him the mindset that he had to go into the Dark Island. Yet this leads me to another conclusion: I think that maybe he wasn't completely in the wrong at Dark Island considering that the others actually agreed to go with him. In the Voyage of the Dawn Treader it says: 

But I hope it will never be told in Narnia that a company of noble and royal persons in the
flower of their age turned tail because they were afraid of the dark." - Reepicheep, VDT 

In this quote, it almost seems like Reepicheep is mocking them or taunting them. He seems to be shaming them for not being as brave as him to venture into the Dark Island. Or he is simply telling them the truth, maybe rebuking them for not being as brave as he thinks royals or knights should be. 

In this Quote it says: 

"Oh, bother you, Reepicheep. I almost wish we'd left you at home. All right! If you put it that way, I suppose we shall have to go on. Unless Lucy would rather not?"
Lucy felt that she would very much rather not, but what she said out loud was, "I'm game." -VDT 

This quote signifies the peer pressure Lucy is feeling. She may have been pushed (as well as everyone else) by the bravery of Reepicheep and did not want to disappoint. Especially considering she is Queen Lucy the Valiant, she may have felt the need to live up to the expectations of that name and with the expectations of Royalty. 

I think Reepicheep was actually right. They were on a quest to find the seven missing lords after all and you can't expect to accomplish something like that without taking risks. Even if they were just exploring it makes no sense to hang back when they come across something that looks like it might be a bit hazardous. If they wanted to be safe they should have stayed back at the Lone Islands, instead of sailing into the unknown with no assurance they would ever find land. 

If human beings had not been prepared to take risks and venture into the unknown Columbus would never have discovered America and Neil Armstrong would never have set foot on the moon. I'm sure Lewis would be appalled by the cult of 'safetyism' that has come to dominate our thinking in recent years.