Please help with water line connection to fridge!!

hello all, I am installing a new fridge and can't figure out how to take out the old water line from the old fridge that's connected to the wall. Can I take the water tubing out or do I have to change the whole valve? To open the valve you pull it up and push it down to open it. I've tried turning it but it just turns in place. Tried pulling it and it won't budge. Dont' know what else to do... Any help would be appreciated!! here is a pic of my problem...

From what I've read, that valve has the tubing attached, and is an accident waiting to happen. Not sure how it comes off, but highly suggest you replace the whole thing, valve and supply line. One of the pros that deals with these should be able to tell you how it comes off. You may need to cut it off. Do you know what kind of supply pipe it is attached to (cpvc, copper, pex?)

On mine, I have what amounts to probably 10' of copper tubing in a big coil behind the frig. It's long enough to pull out like a spring if I need to pull the thing out for service. If you want a hose, get a reinforced SS one.