The chances are if the new pads are binding it is because the caliper pistons are encrusted with mank. For those of us that live in dry climates or don't ride much in the wet this issue is less likely to be a problem but if you ride year round, especially on salted roads, in all weathers the pistons can take a real beating.
The reason brakes release when pressure is no longer applied is that the seals deform when the hydraulic system is activated and then when the pressure releases the hysteresis ofthe rubber pulls the seals back to their original shape moving the pistons back a fraction into the caliper body and allowing the pads to move away from the disc.
If the pistons are coated in a mixture of brake dust, road grime and general filth when the pads are replaced and the pistons are forced back into the caliper body this build up of mank may prevent the free movement of the pistons. Sure when subjected to hydraulic pressure they will move but the crud getting stuck between the piston and the body may well prevent the elasticity of the seal from reverting to its original shape and therefore the pads, while not really having any pressure to speak of applied to them, won't be able to move those few tenths of a mm away from the disc to prevent the rubbing. This problem has been further exacerbated in the last couple of decades by the abandonment of the use of secondary 'Weather seals' on the pistons of modern, multi-piston calipers.
Generally speaking though as long as regular maintenance is carried out the pistons themselves won't degrade so with care the situation is easily rectified.
After the old pads have been removed the pistons can be sprayed with brake cleaner and given a good scrubbing with a toothbrush to remove the build up of mank. Once this has been done the pistons can be pumped out a bit further by clamping all but one of them in place and one at a time pumping the 'Unsecured' one out. Obviously care has to be taken not to pump it out completely, (Although this isn't the end of the world it will require re-bleeding of the brakes which is tedious with some ABS systems.) but they can be pumped out far enough that 'Clean' piston can be seen and at that point the brake clean and toothbrush scrubbing can be applied to the rest of the 'Manky' bit of piston. Once clean and rinsed the piston can now be pushed back fully into the caliper body and the process repeated on all the other pistons in the system, usually there are nowadays eight pistons at the front and two at the rear.
Be aware that as the pistons are forced back into the caliper the fluid displaced will return to the reservoir in the master cylinder end of the system and may overwhelm its capacity so keep an eye on it and suck some out if required. Once all pistons are back as far as they can go the new pads can be installed, the calipers remounted on the bike and the brakes bled in the conventional fashion.
Don't forget to fully prime the system by pumping the master cylinder until the brake becomes firm otherwise you'll have an 'Oh Shit' moment the first time you try to apply the brakes. Now go out and be amazed at how your brakes feel all brand new and marvey again rather than having the sensitivity of squeezing a brick between your fingers!
Pete