If it’s a hinge you need to be sure you are pulling on the But that opens. It isn’t easy when your view in the mirror is blocked by your elbows. It will take a fairy good tug to unclick it to be honest. How long have you had it in? Go back to the piercer if it’s not been in years or you could cause some issues with healing.
Can you get back to your piercer? They would take it out for you and replace it with a labret for free or a small charge. They are a git to get off and I can never do it when my DDs have had them, I always go back to the piercer and ask them to do it.