Edit: See https://en.wikipedia.org/wiki/FairPoint_Communications and https://en.wikipedia.org/wiki/Frontier_Communications
Well, it's not like they were trying to get rid of fiber. Verizon sold off all its wireline operations in rural and non-core areas. Fiber simply went along for the ride.
What Verizon was trying to get rid of was the copper. No company would be willing to buy the copper from Verizon and then compete against FiOS. Thus, the only way that Verizon could get any buyers was to bundle the copper together with the fiber.
This would make it more difficult for Verizon to attempt a market entry at a later date, as it would have to start from a position of no infrastructure.
I remember a Comcast exec a few years ago made the point that it was hard to do deals with Hollywood execs because the execs all lived in places in California that didn't have Comcast service, and couldn't really see the innovations Comcast was talking about.