Since you posted in the Gen7 section, can we assume that you have a Gen7 (2008-2012), or is it possibly a different model year?
To answer your question:
Both wires are at ground potential when the switch is in its resting position. Since you can get it to go down, then the wire that you change from (-) to (+) works just fine when going to (+). It's a 50/50 crap shoot on whether it makes a good contact when it returns to rest, or if the other contact isn't working so well when it needs to change to (+).
To help envision this, imagine your window motor with both wires touching the battery's ground terminal. Nothing happens. When you move one wire from ground to positive, the motor turns as you found out. When you return it to ground and then move the other wire to positive, the motor turns in reverse. The switch just moves those wires for you without having to pop the hood every time. At this point, we don't know and can't determine if the second wire that is moving to positive is not touching it, or if the first wire that should be grounded is actually grounded.
To help find out which is the case, test the plug at the motor while the switch is at rest. Put one lead on (+) and the other to each motor lead. If the light (or meter) responds, then the ground is good for that lead. Now change the tester so that one lead is grounded and test the 2 motor leads again. Have a helper (or use your really, really long arms) move the switch to the known good position (down) and see which one makes the light (or meter) respond. Then move the switch to the up position and test both again. If for some reason they both seem good, the plug it in and see if the window works. It may have just been dirty terminals. But if not, then you now know whether the switch is not sending a (+) or (-) to the motor.
The switch assembly can be removed from the door panel, and then ever so carefully, you can unsnap the switch and inspect it. You can probably even fix it by cleaning the contacts and making sure they're springy enough to work properly. I've done it a number of times (not a lot, just a number
) and successfully gotten windows to move when they wouldn't before. I even fixed one in the parking lot when a friend showed up at a laundromat I used to go to.
The BCM does not control the windows in the Gen7 models.