Why did Shasta care about weather the narnians thought him a traitor once they were able to talk to the real prince corin

Sashta was kidnapped at birth and sold into Calormene slavery who over the course of the book plans to escape from his abusive master with the help of a talking horse named Bree. It is revealed that Shasta is actually Cor, the older twin of Prince Corin of Archenland. His kidnapping was to prevent him from fulfilling his destiny of saving Archenland from destruction.