If you can prove to me, from history, that suppression and violenece will more effectively end the problems caused by fundamentalist terrorists than working to remove the reasons why people become terrorists, go ahead.
The problem is that these "fundamentalists" believe their crusade to destroy the infidel - all who don't comply with the beliefs and lifestyle of Islam - is backed by God. How do you nicely reason with that type of person? They are clearly not interested in diplomacy. They are interested in fulfilling their self-imposed mission from God to wipe the earth of those not worthy. These are their "fundamental" beliefs. To put it succinctly, they are terrorists because they believe it to be their God-given right. Thus, there can be no rational discourse to lead all to peace when their beliefs center around war. Now, if you wish to argue the issue that they supposedly don't represent Islam in their patterns of behavior, then ultimately, they are not "fundamentalists." They are merely acting on a personal conviction, much the same as Adolf Hitler acted on a personal conviction. And, as history would note, the Nazi's weren't stopped by a tea party on the White House lawn.
It boils down to this: Blood will inevitably be spilled. Will it be the blood of the extremists, or that of our own?