Cyclists often do not support segregated bike lanes because of the way they are often implemented. Where's there adjacent parked cars, the lane can become an area where you are just waiting for a door to open.

Still, I've seen very successful implementations, some with a buffer zone between lane and parked car.

I can also believe that segregated lanes (particularly where there's a solid curb or other device) would be safer.

Many cyclists still believe they should be out in the lane. This probably worked ok in some traffic situations, particularly when there weren't that many cyclists. But if we want to scale up cycling traffic, lane sharing isn't likely to support all those new cyclists.