I’m sure it hurts. I don’t think the letter is that bad. It’s a good solid rejection.
Our worst was an acceptance letter–accepted to the school, but not to the major. It was like dangling a giant ice cream cone in front of my son and then telling him he wasn’t allowed to taste it. And then we pursued, as in, “well, can he transfer into this major after proving himself?” And after 3 painful emails with a rude and unclear admissions officer, the answer was no. It felt like, “we don’t want you, but we have some open spots in this other department we need to fill, so you can have one of those if you pay us $$$$$$$$$$. And you’ll be able to watch everyone else have ice cream! But none for you!” That’s how it felt.
Later on he got into a higher ranked (for the major) school. So there!!
Keep your chin up.