A lot of us come out of school wanting to change the world. The four lads from Liverpool really did it.
Partly, it was timing. If they'd started and come to America a little earlier, they'd have had to compete with Elvis before he went in the Army and was huger than huge in pop culture. There was also the feeling in America after we lost John Kennedy, even the teens were feeling it, and here came these fresh-faced kids with catchy lyrics and melodies (listen to "I Saw Her Standing There" and you'll understand, in part, what all the fuss was about) to make listeners feel good again.
The Beatles also were big enough, and good enough, to star in Marx Brothers-like movies about themselves, and so reach more fans or cement their hold on the original ones.
Then of course we had the stuff like Lennon's comment that the Beatles were bigger than Jesus, the drugs, the Maharishi business, Lennon being photographed in the bathtub with Yoko, all of that. Whether they led the cultural change or pushed it from behind, they were part of it, and any cultural history of that time is going to have them in it.