I have read discussion on the same topic in another forum. A couple of things not yet mentioned here is that the OP is experiencing pain and the teacher says it doesn't matter. One of the exercises is to hold down the outer keys (C and G) raise a middle finger as high as possible and strike the key - discomfort at the "high as possible" being considered as ok. Does it matter if the pain is mild discomfort or something more?
Discomfort close to pain sensations? This doesn't sound good me. It's exactly what has given the old finger school its bad reputation. Fingers *can* be lifted without discomfort (especially the index finger, middle finger and pinky, but they should be more or less
straight when lifted, and then come down bent (as the famous teacher Adele Marcus prescribes). In that case there is no discomfort. "As high as possible" seems overkill to me, and is probably a preparation for "striking with force", which is plain wrong. "As high as is still convenient" would be better. I do lots of finger lifting (practising, not playing), but I never "strike" a key. I let the fingers "drop", but it's probably more correct to call it a gentle swing into the key with just enough acceleration to sound the key mezzo forte. The result is a beautiful Lipatti-like sound with lots of pretty (not harsh) overtones, something like the sound of a marimba. It's meant as a workout for the extensors that are greatly neglected in daily life, but that have a considerable workload in piano playing, even if you play close to the key. It's also a wonderful "letting-go" exercise because of the drop after the lifting. It is very, very difficult to do, and it's not something you can let students do without guidance.
P.S.: "Holding" exercises are risky if the teacher forgets to mention how very little you need to keep a key down.
Paul