Ananda Sutta  is a brief but very important Sutta because of a very specific reason: it gives the Buddha’s own explanation of why he remained silent when some questions were asked.

A person by the name of Vacchagotta once visited the Buddha. He belonged to a group of ascetics called wanderers, who flourished in the Buddha’s society. Wanderers were also the wonderers: most of them did not have a firm doctrine of their own, but they were trying to learn from all possible sources in an effort to gain wisdom. Being homeless, wanderers sometimes lived in groups, travelled from place to place, met well-known spiritual leaders, and followed their practices.

After initial greetings, Vacchagotta asked the Buddha, “How is it, sir? Do you accept the existence of the self?”

Instead of answering the question, the Buddha remained silent.
Withstanding the Buddha’s silence, Vacchagotta next asked, “Sir, then, do you reject the existence of the self?”

Once more, the Buddha maintained silence.

Visibly disappointed, Vacchagotta then rose from his seat and left.

The Buddha’s attendant Ven. Ananda also seemed disturbed by the Buddha’s silence. “Why did you refuse to answer Vacchagotta’s questions?” he asked the Buddha.

The Buddha explained to Ven. Ananda that whether he said “Yes” or “No” to Vacchagotta’s question, he (the Buddha) would fall into an extreme. For instance, if he accepted the self, he would fall into the category of eternalists, those who recognized a permanent entity in the person or the universe. Conversely, if he rejected the self, he would fall into the category of annihilists, those who admitted nothing beyond sensory experience.

“If I said ‘Yes’ to Vacchagotta’s question, does that answer go along with my teaching that everything is impermanent?” the Buddha asked Ven. Ananda.

“No, venerable sir,” Ven. Ananda answered.

“Similarly, Ananda, if I said ‘No’ to Vacchagotta’s question, he, who is already confused, would fall into further confusion thinking, ‘It seems that the self I had accepted so far does not exist.’”

Samyutta Nikaya 44.10 (Ananda Sutta)