The stub part of the ball joint is tapered. You have 2 things that can happen; the stub can stay put in the steering knuckle, in which case you can get the nut off, but then need to get the stub out. OR you can have this happen where the stub drops out and it spins. If you follow my suggestion, you can lift the stub back in and then remove the nut, and very often the stub will drop back out when you are through. Have you even tried this? it works, you coulda had it off days ago.....
Gilly

If the taper is actually still stuck and the nut won't "unscrew", you simply need to push up on it while turning.

I'd of the opinion that the taper is loose, though, personally.

A Dremel with a couple cutoff disks will slice through that nut in short order -- make a cut on two sides (you probably can't get exactly opposite) all the way through to the thread, then take a chisel and drive the nut off sideways. This will get it loose no matter what the problem is. You MUST run the cutoff wheel straight, though -- they are VERY brittle and will snap if you apply any sideways or twisting pressure to it.

Leave the shock on and hold the control arm up, though -- if there is spring pressure on there and the taper IS turning with only the nut holding the control arm to the steering knuckle, it will jump down when the nut comes off.

Next problem will be R&R of the ball joint itself. My brother got his out with a 5 lb sledge with no problem, but going in with the new one requires a tool -- either the expensive Benz one or the cheapo Harbor Freight (and a long cheater bar or a good air impact). You may bend the cheapo tool, but it WILL seat the ball joing nicely.

DO NOT HEAT THE KNUCKLE TO REMOVE THE OLD BALL JOINT, PLEASE!!! This is very likely to warp or anneal the knuckle, with serious consequences when the ball joint comes back out while driving.

Peter