See the ultimate problem with this war is that it is a war against an ideology. You can say Islam is bad because terrorists say they are motivated by it, but any objective complaints against the religion's intolerant scripture can be given to any other Abrahamic scripture as well.
If one says we are at war with Islam, they would be speaking against its sharia/salafist sects rather than the entire religion itself. If they do mean the entire religion, then the question comes up of why Islam is less legitimate than other Abrahamic religions.
Ultimately though, the problem is brainwashing. Entire populations including families believe in sharia law. So what do we do? Is Trump right? Do we have to kill them all?