The point you are missing is the point IS want you to miss - ie that they are not represetantive of all of islam , they are a tiny tiny minority of nutcases - ergo their best chance of winning or at least not losing is to provoke the west into acting rashly and in a way that impacts lots of moderate muslims/non IS supporters and enables them to paint themselves as the representatives of the islamic world against west oppression
the flip side is that our best chance of beating them is not to be so f*****g stupid as to play into their hands - the hearts and minds we need to win are not the tiny minority of headcases but the population that surrounds them and the muslim world at large , and we won't acheive that with western boots on the ground in their holy places or bombing the s*** out of no end of civilians.
We also need to win the battle for the hearts and minds of our own muslim population so that they don't become radicalised - and we won't do that by going the route some imbecilic biffers want to go and persecuting or even interning them... the real irony being that organisations like BF and EDF are doing exactly what IS want, and aiding a cause that they claim to despise.
Nobody is representative of all Islam, that's another problem. Winning their hearts and minds means what?