To a Muslim, something that’s “jihad” is by definition a good thing, so when US officials refer to adversaries as “jihadists” we’re implicitly accepting their definition of the conflict as one pitting Muslim holy warriors against enemies of the faith.
I assume Matt is suggesting this is a bad thing, but I’d disagree. We called Nazis “Nazis” and we called communists “communists,” and those were both things those groups called themselves. We didn’t feel like we had to make up some weird, portmanteau name like “Islamofascist” because otherwise we’d be tacitly accepting the worldview of our enemies.
Now, there are other possibilities, like “Salafist” and “takfirist.” And when I use the j-word I usually prefer “violent jihadist” since (a) I don’t have a problem with Muslims peacefully trying to convert people to their religion and (b) it makes it clear that we’re objecting to military jihad, not the internal struggle for your soul. But in any case, I don’t see a problem with using the word that radical Islamic militants use for themselves. That seems like a feature, not a bug. Our job is to convince Muslims that violent jihadism is a bad thing, not to pretend that it doesn’t exist.