@Scruffylexi time to stop thinking about “what might have been” and focus on what is. My son had a very deep disappointment also at this age, and the lesson you want them to learn is “hard work pays off” or, “perseverance pays off” not “you work hard, you do everything right and life is not fair”. The latter makes the kid a victim of circumstances, and the former lets the kid know they can affect what happens to them.
It is very tough when you are in the middle of this, and still feeling the rejection, which is why I’m writing. I have the benefit of 5 years of hindsight and can see that actually, that disappointment ended up being probably the single best thing that happened to my son. It sure didn’t feel that way at the time, and I sure didn’t see it, but now – it actually is crystal clear.
However, it all depends on how you the adult frame it. Also, I’ve learned not to focus on the outcome, but the process. If my son has done the best he could, put in his best effort – then, that’s all he can do. After that, whatever happens, happens, but he can be proud of the work he put in.
So for next year, consider emphasizing the process. For example; “I am so proud of the essays you wrote for Choate! You worked hard on them, and they are some of your best writing I’ve seen. Well done. If Choate accepts you, or doesn’t accept you, you can know you’ve done the best you can. Good job!”
Finally, I haven’t followed your journey and don’t know what schools you applied to this past year, but consider widening the net. One of my sons went to a second (or is it third?) tier boarding school and while it was a different experience to the tippy top boarding schools, it was a truly fantastic, formative experience for him, and he ended up at a great college too.
Good luck to you, it is hard when things don’t work out, but take the long view and I know they will in the end.