When i changed my oil the first time, i used an old leather belt to twist the filter off. It's an age old mechanics trick that my old man taught me. Just make sure you have someone hold the bike, otherwise you might be changing plastics too.
I have found the oil filters are always hard to remove on the FZ6R.
I had to get a filter remover that goes on the end of a socket wrench. I got it at Autozone. It fits over the end of the filter and has two metal clamp-like pieces on either side so as you turn it, it clamps harder onto the filter.
Not sure if you're filter is too damaged to use something like this at this point. For next time, get a filter like K&N that has a nut welded onto the end so you can just wrench it off.
my first time, it was hard as hell to get off also! mine was bent to shit when i was done! someone torqued it so much, that even after being forced to buy a cap piece with the nut to go over the filter so i could use a small breaker bar... the oil filter actaully started to twist! not by coming lose, but scrunching and twisting (it was that tight!)...