Final answer:
There is a difference between Daniel's opinion and Mr. Miyagi's opinion about continuing to fight. Daniel wants to continue fighting while Mr. Miyagi advises him to quit. Daniel is trying to prove himself to Mr. Miyagi.
Step-by-step explanation:
The difference between Daniel's opinion and Mr. Miyagi's opinion about continuing to fight is that Daniel wants to continue fighting, while Mr. Miyagi advises him to quit. Daniel is trying to prove himself to Mr. Miyagi, not to his parents. After getting injured, Daniel believes that he still has something to prove, and he wants to prove himself to his mentor, Mr. Miyagi.