It's an even harder job to get.
Think about it this way: let's say for argument's sake that there are 30 new Broadway shows (plays and musicals) next season. Also for argument's sake, let's say that there are 4 major casting directors that generally cast all productions for Broadway. Finally, for argument's sake, let's say that the average cast size is 10 actors.
Do the math. That means 4 casting directors need to hire 300 actors.
You tell me which job is easier to get: an actor or a casting director?
The one advantage is that there are less people trying to get that casting director job than there is getting those acting jobs.
So here is my advice:
#1 Remember that Broadway is only an avenue of the theater spectrum. There is theatre all over the WORLD. There is commercial theatre and not-for-profit theatre. There are sit-down productions and there are touring productions. It helps if you decide first what you want and don't want. If you KNOW FOR A FACT that you're not suited for touring, then that's one less niche you have to worry about. Pursuing jobs for each of those theatre niches is very different.
#2A Once you narrow down where you want to work in there (and by "where" I mean what continent, region, state, or even city AND THEN commercial or not-for-profit), then seek out internships in that exact area. An internship will a) establish contacts, b) teach you the incidentals of running the office while gaining insight into that part of the business, c) give you experience for your resume, and d) be an eye-opening experience for yourself to see if it's what you REALLY want to do.
#2B Most offices do not want to hire interns that are in high school, but high school interns are not as uncommon as you think. Before you go out into the professional world as an intern, make sure you are PREPARED. It's a good start to know the basics of Word, Excel, and Outlook...but if you want to be taken seriously as such a young age, you need to really WOW them when you apply for the internship. You need to at least be at an intermediate-to-advanced level in Excel, Outlook, and Word (in that order), you need to learn how to make coffee, file, have a professional voice and vocabulary when answering phones, etc. Basically, you need to learn how to work in an office setting. SO my advice is to get a summer job in a NON-THEATRE office and learn those basic administrative skills FIRST, then once you acquire all those incidentals, you can then try for an internship. At your age, you'll be ahead of the game.
#2C You might be thinking... "What the hell? Why would I need to go through all that to be a CASTING DIRECTOR???" To that I say this: yes, a Casting Director is just one of many jobs in the artistic side of theatre. You need to have those artistic abilities, definitely. BUT to get to be a Casting Director, you have to climb ladders. And the bottom of that ladder (in fact, the first 2/3 of that ladder) are people who spend most of their job in front of a desk.
Good luck!
"The Spectacle has, indeed, an emotional attraction of its own, but, of all the parts, it is the least artistic, and connected least with the art of poetry. For the power of Tragedy, we may be sure, is felt even apart from representation and actors. Besides, the production of spectacular effects depends more on the art of the stage machinist than on that of the poet."
--Aristotle
