Working on my daughter’s 2007 Forester X , front disc, rear drum. Bought it used and it had semi metallic pads on it from the previous owner. Brakes felt weak so I bled them.  Once I did, she started to get a grinding/scraping noise from the front, but the brakes were better overall. I pulled the calipers off and put ceramic pads and new hardware on it, cleaned up and greased the slide pins too. Still made noise but only after they got hot. I bled it all out again and pulled the calipers to work the pistons out and pressed them back in 4 times per caliper. Then it was better, really had to work at getting them hot enough to get any noise but it was still there. As soon as you touch the brake pedal the noise stops and the car stops great. But as you drive off, grinding and scraping. Nothing is touching the rotors but the pads. I honestly can’t tell if it’s both sides or just the left, sounds more like the left inside the car. 
I’ve never run into this. What’s next, both calipers or master cylinder? 
thanks

1. Check the pad clips. They may be bent or have rust on the caliper which pushes the clips out a little. I’ll remove clips and make sure no rust is bubbling under them on the caliper bracket. 

2. hose collapse. If a flexible rubber hose collapses internally it’ll prevent the fluid pressure from backing up and the caliper can’t release fully. The brake booster provides enough pressure to push through it. It’s not very common on Subarus. 

I highly doubt it’s the master cylinder. 

I did clean up the calipers before installing the clips and pads, but I’ll get some hoses . 
Thanks

No chance it’s a dust shield rubbing somewhere that changes with heat and brake use? 

Other thought is the wheel bearing is on the way out. Worth jacking the wheels off the ground and checking for bearing play. 

Cheers 

Bennie

Did you notice the old pads wore evenly when you pulled them off?  There's one pin that has a rubber damper inside, that tends to swell and cause pads to wear lopsided.  It eventually causes sticking issues because the pressure is more like a parallelogram than square.  I remove those when redoing brakes.