This is a phrase that gets beaten to death in arguments, as in, “I don’t understand why you think…” People use this phrase as if they’re introducing an accusation, when they’re only stating their ignorance!
Perhaps this is meant to be employed as a rhetorical device, trying to get someone else to draw out a defense of a position that you don’t think they really can defend, thus exposing their weakness. (“I don’t understand why you believe that the moon is made of green cheese.” “Well, it’s obvious, actually. You see…”)
However, that’s not how it seems to be used most of the time. Whenever I hear someone say this, it’s always delivered in a tone that suggests that the speaker’s confusion is inherent proof that there is no rational explanation behind whatever proposition they haven’t bought into. But since when is a failure to comprehend on one person’s part somehow evidence against the claims made by someone else?
Such a reaction as “I don’t understand…,” intended to convey skepticism more than curiosity, strikes me as a singularly solipsistic excuse for an argument: “I have no real rebuttal to your proposition, but I just don’t like it, therefore it’s wrong.”
Gently Hew Stone 
Well said!
P.S. I’m a binge reader and love your writing style. What advice could you, as an English teacher, give to those of us that have graduated high school but would like to improve vocabulary, grammar, and overall intelligent-ness (see what I mean) of our discourse?