I don't think anyone actually argues that "our insensitivity" is why groups like ISIS exist and engage in terrorism. Rather, what is being argued here is that, in our zeal to fight the terrorists who operate under the banner of "radical Islam", failing to treat a religion of over 1 billion followers with nuance will only reinforce the appeal of groups like ISIS to those young Muslims who might be considering joining such a group but still have reservations about it. In other words, if we don't act with caution and sensitivity, we would just be proving the extremists correct, that we really are at a war with all of Islam.
Also, just for the record, both "sharia" and "jihad" have much broader (and more legitimate) uses within Islam than the way in which the violent fanatics use them - which is the usage that Americans are familiar with.
