I love this thread. it’s a tough moment for sure!
Some language that has proven helpful for disappointments in our home:
You did your part. Your job was to make yourself part of the conversation, and I think we both feel confident you did that. What they did with that is really out of our control. But you showed up, you made it really clear what you were offering, and you made yourself very admissible if they were looking for someone like you. Your job isn’t to guess what they need or want, but to make it really easy for them to say yes if they want your profile. You did your job extremely well.
I’ll add that we also talk about the whole process in terms of “knowing what you bring to the picnic.” So knowing yourself, and knowing what you bring to the party is key (in life, I believe, not just college admissions). And so you show up with your very clearly-communicated picnic basket and you walk around the park and find the school that wants your picnic basket to join their party. so the ONLY “failure” is 1. not doing the work of making your picnic basket truly represent you, or 2. not doing the work of making the picnic basket crystal clear to the ones peeking in and deciding if they want your basket to join their party. (Do NOT make the admissions people have to become a sleuth to put together the narrative of your picnic basket for you – they don’t have that kind of time. You need to do that. ).
It is amazing how much easier it is to live with rejection if we feel super good about how we curated and communicated our picnic basket. It stings, BUT it doesn’t also come with the “oh but what ifs…” that can linger in our heads and hearts for a very long time.
so that is our approach – it’s actually making sure the picnic basket is done right, and that it is truly a reflection of the deepest most amazing parts of the applicant. :). Rejections are much easier to move past, even the ones that truly rip apart someone’s dreams that felt SO CERTAIN and SO RIGHT. 
(been there more than once in our household over the years for sure…).
What we personally do NOT find helpful is any version of toxic positivity such as “everything happens for a reason” or “trust the process” or “you weren’t meant to go there.” Another unhelpful approach is to immediately push another school. A little space and time does wonders. And then…gentle nudges into other schools have been helpful, BUT it’s an art determining how long to let the moping go. :).