In plain words
So, in the gurukula, the gurus of those days taught the Ātma-tattva along with such food and such a way of living.
Into this gurukula came Yājñavalkya. He was a man of keen intellect. He had a very quick mind. The lessons of each day he learnt that very day and recited back to the guru. The guru was pleased with his cleverness. People began to say among themselves that he was very clever, a man of great intellect. In this, Ahaṅkāra began in Yājñavalkya as a small seed. In my class there is no one else who brings better marks than me. Of all the questions the guru asks, there is no one but me to answer them. I am the one who has taken the 'O' grade. By the time Ahaṅkāra arose, it had become a zero grade. Here, by the time Ahaṅkāra began, some carelessness too entered into Yājñavalkya. Along with carelessness, incivility too came into it. Vaiśampāyana went on noting all this well. The gurus of those days would give even their lives for the good of their disciples. Those who had such bad traits, going astray, behaving with discourtesy, going about without śraddhā, they punished very strictly. Śikṣā means education itself. Education is not merely reading books. True education is to bow to the guru's command and accept with all one's heart the punishments he gives. So Vaiśampāyana, who had noticed all this, called him near one day: 'Yājñavalkya! You are not fit to study in this gurukula. Leave it this very moment and go. And not merely leave: you must give back to me all the learning I gave you, and then go,' he said. With as much Prema as he had given his learning to his disciple, with words as harsh he took that learning back again. Yājñavalkya, who understood all this, vomited up all his learning. Tittiri birds ate what he had vomited. So those birds too began to chant this Veda. Because the tittiri birds chanted it, this Veda was named the Taittirīya Upaniṣad.
There are two kinds of sāmpradāya for the Vedas. One is the Brahma-sāmpradāya. The second is the Āditya-sāmpradāya. The Veda that Yājñavalkya vomited came to be called the Brahma-sāmpradāya.