PGP was considered dangerous because it could have allowed Soviet spies and military officers to plan the nuclear annihilation of the western world without the CIA realizing what's happening before it's too late.
Time for some history.
During World War II, the importance of cryptography for military use became apparent. Being able to crack enemy cryptography while also having cryptography systems for oneself which can not be cracked, proved to be an important military factor which could result in victory or defeat.
During the subsequent universal arms-race during the cold war, all sides were aware of this. Having the upper hand in cryptographic technology over the other side was considered a strategical factor which could turn the tide in another world-war. That meant that any knowledge-transfer of cryptography know-how from the Western to the Eastern world had to be prevented.
As a result of this doctrine, cryptographic technology was considered of military value and thus filed under Category XIII in the United States Munitions List. That meant any data storage medium which contained cryptographic software was legally considered like live ammunition when it came to moving it across borders.
From today's point of view it might seem absurd to try to contain knowledge through export restrictions designed for physical goods, but it fitted into the isolationist viewpoint of the military strategists of the cold war era. Also remember that this was the 70s, long before the internet age. This was decades before the time where you were able to obtain any software in the world via the internet through your favorite piracy website. Getting a piece of software from computer A to computer B usually meant to put it on a physical medium like a floppy disk, magnetic tape or (even earlier) punch-cards, and the movement of such physical media across borders seemed controllable (at least in theory).
Technology marched on. In the 80s, the first international computer networks emerged, and the hacker community began to flourish. The world became increasingly interconnected and soon it became apparent that containing knowledge within geographical borders was an exercise in futility. But as usual, politics and laws didn't keep up with technical innovation, so when PGP emerged in the 90s, it was still subject to cold war era laws regarding cryptography exporting. The algorithms it used were open secrets, available to anyone in the world capable of buying a modem and making long-distance phone calls. Hackers were tattooing them on their bodies to ridicule the cryptography export restrictions. But as a commercial company, PGP had to play along and find a loophole in the form of exporting their source code in printed form and re-transcribe it.
Although the restrictions on cryptographic technology have been relaxed in the past decades, some of them are still in place.