How to open a malfunctioning tamper-proof bottle cap?
I've had this before, and solved it by breaking the join  between cap and ring with a small screwdriver, one section at a time.  Long nose pliers may be handy towards the end.  You might manage to get the tip of a butter knife in the join instead of the screwdriver.
Trying too hard when it's not coming off tends to deform the threads in the cap, so it may not go back on securely later - you might need to decant the contents.