Why Can't a Third-Fruit Anāgāmin Have the Thought "I Am a Third-Fruit Person"?

Original text of the Diamond Sutra:须菩提。于意云何。阿那含能作是念。我得阿那含果不。须菩提言。不也。世尊。何以故。阿那含名为不来。而实无不来。是名阿那含。

Literal translation: The Buddha said to Subhūti: What do you think about this? Could an anāgāmin have the thought, "I have attained the fruit of anāgāmin"? Subhūti replied: An anāgāmin cannot have such a thought. Why is this said? Because the anāgāmin is called "one who does not return," yet in reality there is no dharma-mark of "not returning" — that is, the matter of attaining the fruit of anāgāmin; "anāgāmin" is merely an expedient name.

One who has attained the third fruit has a mind even emptier than that of a second-fruit practitioner, and has no thoughts of "I am such-and-such"; therefore he will not constantly think, "I am an anāgāmin." If it were otherwise, the mind's thoughts would not be empty, and he would not have attained the anāgāmin fruit. Because an anāgāmin possesses meditative concentration (dhyāna) of the first dhyāna and above, after death he is reborn among the five Pure Abodes (ākaniṣṭha heavens) of the form realm to continue cultivating the path, attains the fourth fruit of arhatship in the five Pure Abodes, and directly enters Nirvāṇa without remainder, no longer returning to the human world; hence it is called the fruit of non-returning, also called the fruit of "not coming." In reality there is no such thing as "not coming to the human world" — neither coming nor not coming actually occurs; both are illusory, false appearances. Giving such a false appearance a name, it is called anāgāmin, called the third fruit. Therefore one must not think that there truly is an anāgāmin fruit to be attained, must not think that a third-fruit practitioner truly exists, and must not give rise to a grasping mind (upādāna) or an arrogant mind — otherwise one would not be a third-fruit practitioner.