The terrorists that do mean us harm can come from the rest of that innocent population. Using brutal tactics, IMO, serves more to swell their ranks than as a deterrent.
Again, this is an unfalsifiable claim. If killing terrorists wherever we find them reduces their number by, say 90%, you could always claim that making nice to them would have reduced their number by 95%. If we could somehow kill them all, you could claim that it could have been done faster and cheaper by making nice to them.
And, of course, if the number of terrorists were to actually rise, you'd point your finger and say, "See? It's just as I told you!" Your claim (and it's not just yours - I'm simply responding to your post) can not logically be disproved.
There is, however strong logical and empirical evidence that your claim is wrong.
The logical evidence:
We keep hearing that the Islamists are only a tiny minority of all Muslims, that the vast majority of Muslims disapprove of fundamentalist Islam because it is just as intolerant of mainstream Islam as it is of Christianity. The Taliban were noted for their viciousness against traditional Afghan Muslims; Al Qaeda in Iraq lost a lot of its support when it became apparent that they were just as happy to torture, maim, and kill Muslim Iraqis as they were to torture, maim, and kill American soldiers - perhaps even more so.
So if the vast majority of Muslims in fact want nothing to do with murderous Islamists, and in fact live in fear of them, then why would the fact that someone is killing Islamists "swell the ranks," as you put it, of the
jihadis? That is not logical.
The empirical evidence:
Al Qaeda in Iraq was noted for its brutality. The Bush/Petraeus surge succeeded in virtually destroying al Qaeda in Iraq. Fighting the Islamists in Iraq, far from "swelling their ranks," had the effect of uniting local Iraqi tribes to join the fight against al Qaeda in Iraq, and provide for their own local security, in the "
Awakening Movement." If fighting al Qaeda in Iraq was going to swell the ranks of the terrorists, then the "Awakening Movements" should never have happened (and note that the first "Awakening Movement" was the idea of a Muslim tribal leader - it did not come from the U.S.).
Note that my claim is not falsifiable either. But at least I have evidence to support it, as opposed to the increasingly tedious repetition of the chant that, "Killing terrorists only increases their number." If you think so, show us the evidence.