On TNG episode Brothers I'm kinda siding with Lore. Why did Noonien Soong create a whole other Android instead of just fixing the one he had? I don't know how that's the logical choice and I can see why Lore thinks Soong is favoriting his sons. Why disassemble Lore instead of just powering him down and fixing his malfunction?
Data was built in reaction to the colonists' fear of Lore.
Lore was made to be as close to human as possible, complete with emotions. He was unstable, however, causing the colonists to pressure Soong to deactivate him. The early design, coupled with the general unpredictability of emotions and a superhumanly strong and fast android....well, you can see why they were concerned. Data was made to be a less threatening iteration of Lore.
Lore was a prototype
Lore was Soong's first success in creating a positronic brain; his previous failures are what led to his going into seclusion to continue his work. As a prototype/proof of concept, naturally Lore's design was not perfect. He functioned, but not completely to spec, partly due to the unpredictability of emotions, but also due to some integral design flaws that likely exacerbated the problem.
Data is the result of Soong's refinement of that design, and the removal of the destabilizing element - emotions.
Soong didn't know how to fix Lore - yet
As some of the comments to the original question indicate, solving the problems with Lore necessitated a clean start, as the issues were at such a fundamental level. It was less an issue of fixing the prototype, than improving the overall underlying design. By removing the destabilizing elements, Soong got a cleaner, simpler design to work with and improve on, which made it easier for him to eventually figure out where the original design went wrong. He could then take those lessons and apply them to Lore.
This is also why Lore wasn't simply destroyed - Soong needed time, and additional data (pun intended) in order to learn how to fix Lore. This can be seen in s4e3 "Brothers": Soong developed an improved emotion chip for Data, with the intent of porting it over to Lore if it is successful.