Why didn't Jim agree to "run for it" with Dr. Livesey

Jim did not agree to "run for it" with Dr. Livesey because he gave his word to Silver that he would stay. He was a man (young man) of his word.

"Hawkins, will you give me your word of honor as a young gentleman—for a young gentleman you are, although poor born—your word of honor not to slip your cable?”

I readily gave the pledge required.