Why Do Lefties Dismiss/Discount/Downplay the Jihad?

Long story short: It's because of Leftist guilt/masochism/useful idiocy:

Liberals cannot understand so much hate against us. So liberals sympathize. Liberals help find the answer. They join in. To justify the hate. 

By hating ourselves.

One more reason: they're narcissists who have to be seen to be sympathizing with the "less fortunate" so that everyone will view them as paragons of virtue, an amalgam of, say, Mother Theresa, Gandhi and the Dalai Lama (or maybe Oprah and Deepak Chopra).

When in fact they're huge narcissists with an ego the size of the Islamic State.