I tried to understand why walking downstair hurts while walking upstair is good. All I found in the internet were website while keep saying the pointless fact "It's runner's knee" and didn't try hard to explain why except telling you may have a feet in bad shape.
I think the knowing of the kind of muscle/joint/ligament involved during walking upstair/downstair might help understanding the cause of the pain.
From my personal experience, I trained my quadriceps by squating and my pain goes away temporarily. If I let my quadriceps relax for 2-3 weeks and try to run, my pain comes back. So I think it must related to the muscle.