Because in a Dan Brown book, some secretive group has to be hiding a secret from the rest of us for centuries, or there is no reason for people to chase Langdon all over (location of choice) with (girl of the moment). Meh.
Will Read Anything has it exactly right. There has to be a secret elite with the higher knowledge that's too scary for the common herd to possess, and/or can't be revealed to the evil enemy. And there had to be someone from the elite to push Langdon through the ridiculous concluding 50 pages or so-all religions are the same, with the same exact guiding principles, and so the Bible is the repository of the secret hidden knowledge, and we will all learn that we are God/gods and understand the ancient mysteries, as soon as we accept the 100% proven wisdom of noetic science. Just go look at the cap of the Washington Monument in the sunrise, and all will be revealed. (You and my sister go on without me; I should go the hospital since it's been more than 24 hours since my hand was cut off.) Peter Solomon is the deux ex machina.
Interesting fact I picked up about the Washington Monument cap: "Laus Deo" is not the only thing engraved on the aluminum tip of the capstone. The other three sides have details about the production and installation of the capstone.
SO, in the book, it is implied that for every ancient religious, philosophic, or spiritual tradition, there is some secret knowledge that will enlighten all mankind SOMEDAY, but for now those secrets MUST be kept from the average person; consequently, there arise secret societies which make a religion out of their guardianship of such knowledge; but WHO decides when and how the info EVER gets released, and how do they intend to call off their watchdogs when the time is right? I just couldn't get whether the secrets were supposed to be revealed, or not. It's like Brown couldn't make up his mind. I think it would have made a much more interesting story, if the Masons had wanted to open their doors and reveal their mysteries, but were thwarted by their overly-faithful few who are compelled (or enjoy power positions) to keep everyone in darkness.
The OP raises an interesting point yet I'm not sure I agree with Cory Warren. According to the book, the capstone remained wrapped and sealed for a long time which means Peter couldn't have solved the ENTIRE pyramid. The only way he'd know is if someone TOLD him.
Dan Brown told him. And he shouldn't have done that because it is going to get him in big trouble. That's why they won't let him tell us anything. But if you can find a blackmarket copy of the "actual" book that Dan Brown wrote, maybe you'll know as much as Peter "Solomon" did. Or maybe you'll realize that the 10 hours or whatever it takes to read this book, and the blackmarket copy that you will soon be looking for, is time you will never get back.