When Daniel walks into Mr. Miyagi's workshop and asks him if it was he who fixed his bike I always wondered to myself what was wrong with his bike. Yeah, he said he hated his bike and threw it into the dumpster, but what was wrong with it?
The book clears it up.
Chapter 8, page 35
"KIAAIIIII!" Daniel howled in disgust as he heaved his broken bicycle into the dumpster outside his apartment.
He had walked it all the way home, but when the axle broke in the parking lot, he gave up on it.
Daniel's mother was getting out of the Chevy when she saw Daniel at the dumpster.
"Daniel!" she called, running across the lot to him. "What's the matter?" He turned away from her to hide the tears and the bruises.
"What's wrong with you bike? Why did you throw it away?"
"Felt like it," he mumbled.