I have tried turning counter clockwise but to no avail. Is there some other secret? I have another horn button to put back, so I could deatroy it. Only replacing because there is a big chip out of it, maybe from where the PO tried to remove it. thanks for any advice.

 

I believe you have to push in the button while turning counter-clockwise.

 

Fred is correct, just push in and turn. I would caution about being destructive in removing the original. Unless you can convince only one part to be affected by brute force, you'll likely create a bigger challenge for repair.

Good luck.