Removing the flexi-tail is a bit of a puzzle box and reveals the ingenius design of the attachment. The brass clip has three barbs, each set at a different distance from the tip. The female receiver in the faucet body has three groves set at the same increments as the three barbs. When the male is inserted into the female, each of the barbs latches into its designated groove. The barbs can spin in their groves and the male end of the flexi-tail can spin inside the brass clip. If that were the end of the design, you would not be able to remove the flexi-tail without destroying something.
So here is the cool part. Each groove has a ramp in it. If you spin the brass clip, the barb is forced to ride up the ramp. If you pull on the flexi-tail at the same time, the barb will pop out of its groove and catch in the next groove. The ramps are spaced in the receiver so that all three barbs hit a ramp at the same time. So to remove the flexi-tail, just spin the brass clip several turns while pulling on the tail. On the third pop, it will come right out. The brass clips is not easy to spin. Use a screw driver to push on the little tabs at the base of the brass clip. You may need to tap the screw drivers with a hammer. The whole operation is easiest with helper to maintain tension on the flexi-tail.