If it's cup and cone style, are you sure you're working on the adjustable side and not the fixed cup?

If it's a cartridge unit, make sure that you work on whatever side the adjustable ring is. Some models have the fixed side with the flange on the drive side, some NDS. Phil has no flanged side at all. Of course if you can't get one side to go, you can work on the other side. I believe if you have a new Shimano with the plastic ring, you should always work on the metal side.

If you're doing all that and it's still not working, get a long bolt or piece of threaded rod (hint: old nutted axles are often the right size) and bolt it through the top of the BB tool so that the bolt cap/a threaded on nut will keep the tool in place and not slipping out.

Now get your favorite way-too-big wrench and a cheater bar if you got it. Go to town. A few whacks with a hammer on the handle can often break the corrosion that's holding the thing in place.

I was in a shop once. They had this bike with a Phil BB in there with the recommended loctite. They had a 6-foot bar on the end of the wrench and still could barely get the damn thing to budge.