The Buddha’s most radical disagreement with the Vedic traditions of his time was on this point. Atman, in Hinduism, is the true self that is identical with Brahman. The Buddha taught Anatta — that no such unchanging self can be found.
The argument is empirical: look for the self among the aggregates of experience (form, feeling, perception, mental formations, consciousness) and you will find only processes in motion. There is experience; there is nothing permanent having it.
Whether anatta and Atman ultimately disagree or name the same dissolution from different angles is a contested and productive question.