The SUV faced plenty of competition, especially in the form of Honda's CR-V and Toyota's RAV4. But what I believe held down sales was the tall grille element on the vehicle's front. For one thing, it was unrelated to nearly all previous and current Subaru grilles (exception: the 2006 Imprezia WRX STI). And at the time, it struck me and apparently many others as looking odd, providing the front of the car with a kind of snout.
In retrospect, and in the images below, the appearance of the front doesn't seem so bad. Many other designs over the past several decades have included tall central elements, so the "shock of the new" couldn't have been in play. So it was just one of those things; you had to have been there when the Tribeca hit the streets to get the negative vibe.