I can't see why this dose not compress the spring , it only has to clear the collets which I can clearly see it dose in the photo . My guess is that the collets are stuck in the tapper which will stop you compressing the spring . As I said you may need to place a socket under the valve head then give the valve cap a slight hit with a hammer to release the collets from the tapper. Not too hard you don't want to bend a valve.

