Yeah, it can be quite tricky
You need to push hard enough on the pad so you're actually pushing the plastic ring the pad is mounted on - best way seems to be to hold the cup in the palm of one hand and push into your palm 'through' the pad with your other hand. Then, applying lots of pressure, twist anti-clockwise.
There should be no danger of breaking the plastic cups, but if the pads are old, I guess there's the risk they might tear ...