More reliable braking, stronger braking, not wearing out the rim, easier to remove wheels for cleaning / punctures... etc.Why would anyone want a disc brake on a road bike? bulkier, heavier and probably would cause some drag also. I personally can't see a use for them on a road bike.
The negatives above I just don't see as issues. Bulk is irrelevant, weight difference, if there is any, is not material enough to concern me and I find them much easier to set up than rim brakes.
IMO, disks are much better brakes in every meaningful respect. I don't expect, or want, everyone to agree but, at the moment, those who do want them just don't have much choice beyond a handful of cx-style bikes.