This is likely "Generation Gaps" (1972) by George H. Smith, writing as Clancy O'Brien, in the September 1972 edition of Analog.
The story opens on an Earth-Moon shuttle and we're introduced to one of the titular gaps as a younger (20ish) stewardess tries to ply Prof. Morris Benjamin, who is much older (50ish), (and very much uninterested) with drugs and free sex. After she gives up she sends the older (40ish) captain to talk him out of abandoning Earth and going to live on the Moon.
Earth has apparently been given over to the Aquarians, and university teachers (like the protagonist) are reduced to teaching the history of rock music, astrology and the I Ching.
The story then flashes back to a representative from the "United Communes" coming to his office to try and convince him to stay on Earth because ever since the "Jerries" (older square folk) have started leaving, things have started to break down.
We then learn about the following generation: the Pyros who burn things, the Vamps who want to be vampires and the Eaters, who practice cannibalism.
When the shuttle arrives on the Moon, the captain suddenly defects as well, bringing with him his 5-year-old son. He promises that he has hidden his son from society, so he has never been exposed to drug culture or the rampant other vices of society. (The son even has a short hair cut!) He escapes even as the rest of the crew of the shuttle try to keep him from defecting, since without the captain they have no hope of operating the shuttle.
He caught up with me, his breath coming in short gasps as he clung tightly to the child in his arms. "I raised him in my cabin on the ship... he's never set foot on Earth... he's never had drugs... never heard the music... never listened to the superstitions... so I think he'll be all right."
"Of course he will," I said
The story closes on the end of his conversation with the government representative:
The youth-hell, he was thirty-five!-had told me about their thems, the fifteen-year-olds who were coming up behind his generation and how terrified the gurus were of them.
"Don't leave us," Little Running Rabbit had said. "They're coming up behind us and we don't know what to do about them. We need help. For God's sake, don't leave us. These kids are really spaced out and we don't know what to do."
I had tried to hold them back but the bitter words had come. "You raised them!" I told him. "You raised them your way... not our way!"
Then he had hurled the words at me, the words that were at once a barbed missile and a stinging indictment.
"But you raised us!" he had said.