Cooper began writing novels because he thought he could do a better job than the novelists he was reading.
Here's why the original sentence was incorrect:
* "that was reading": This phrase is missing a subject. It should be "that he was reading".
* "novelists that": This phrase is missing a verb. It should be "novelists he was reading".
The corrected sentence clarifies that Cooper was comparing his writing abilities to the novelists he was reading.