Photo Credit: Giovanni Rufino / The CW
Dan and Vanessa are, I guess, both applying to the Tisch writing program, but Vanessa isn't telling anybody that. I guess because it would take away her entire persona as a guerilla documentarian or whatever, but also because that's sort of Dan's territory. So they spend the whole episode refusing to critique each other's work, like they usually do so fearlessly, because it would interfere with their Relationship.
Of course, once the truth comes out -- that they are both horrible writers, obviously, and hate each other deeply -- they are free to resume their Relationship with no ill effects. Although it seems possible (and having seen some of Dan's writing for ourselves, more than likely) that Vanessa has gotten in by episode's end, while hopefully Dan has not.