The question of why you want to write a particular story tends to arise mostly when you're doing speculative work. That's not to say it does apply to commissions. When I'm pitching a novel to an editor or publisher, I still need to convince them there's a story worth telling and that I'm passionate enough to deliver upon the promise of the premise. [For non-fiction pitches, you need to demonstrate why YOU should be chosen for a particular project.]
But why you want to write a particular story is fundamental to doing good speculative work. [Apologies for any mistypings, thumb still on the blink.] If you can't get excited about the story you're trying to tell, why should anyone else? If you don't have passion for your concept, your characters, the world you're creating, most likely it'll seem lifeless, manufactured, false. You can fake it, but you won't fool all the people all the time.
This week the next stage of my work for the Lighthouse TV drama course is due in. By Friday each writer [or writing team] must submit a 10-page treatment for their original TV series idea. Characters, individual story ideas, the concept, the world of the show and where I think it would go in a second series all need to be included, along with a detailed synopsis of the opening episode. So it's time to make decisions, nail down some choices.
Crucially, do I want the pilot to be a typical episode, redolent of what the show would be like week to week? That's the hit the ground running approach, as used in such pilots as CSI, Mad Men and Hill Street Blues. Or do I want to spend the pilot establishing the premise of the show, so that the second episode would be more typical? Examples of this are Life On Mars, The Street and Clocking Off. I'm probably leaning toward the latter.
Why? My proposed show is quite high concept, so there's a fair amount to set up. I like to see a protagonist transformed by events in a pilot, their ordinary world disrupted - probably because it replicates the classical storytelling structures. On the other hand, a show like The Shield has a great episode of the week pilot and only reveals the backstory of how these characters came together for a later episode [ditto The West Wing].
Like I said, this stage of the process is all about decisions, a thousand little choices that all contribute to a bigger picture. That's why you need to know why you want to write this particular story. If you don't, you risk being paralysed by indecision over every little one of those choices. Onwards!