Throw out bearing chatter

I have a 1985 Alfa Romeo Spider. I seem to have a chatter coming from the throwout bearing. I have replaced the clutch pressure plate and throwout bearing. I then replaced the clutch master and slave. I seem to have a chatter from the bearing now. It is like the bearing is chattering against the pressure plate. I can push against the clutch for with my hand and it stops chattering. Soon as I push the clutch and release it starts again.

My question is: Is the throwout bearing supposed to release completely from the pressure plate or should it just ride against it when the clutch is released. I really enjoy this little old car and hope that I can keep it running.

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I am wondering if the clutch slave cylinder is loose, incorrectly adjusted or not positioned correctly. Another thing to check is whether the throwout bearing arm is firmly seated on the pivot. Usually there is a spring clip that holds the arm against a ball and that may have popped out.
One more thing, is the bearing correctly and firmly attached to the arm or holder?
It may be necessary to pull the transmission to check some of this stuff which, as we know, is not fun!
Good Luck.