Why Can't an Anāgāmin of the Third Fruit Have the Thought "I Am an Anāgāmin of the Third Fruit"?

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? Can a non-returner (Anāgāmin) have the thought, "I have attained the fruit of a non-returner"? Subhūti replied: No, a non-returner cannot have such a thought. Why is this so? Because a non-returner is called "one who does not come," yet in reality there is no such dharma-mark as "not coming"; this is merely called a non-returner (Anāgāmin).

One who has attained the third fruit has a mind even emptier than that of a second-fruit practitioner, without any thoughts of "I am such and such"; therefore they would not constantly think, "I am an Anāgāmin." If it were otherwise, the mind would not be empty, and the fruit of a non-returner would not have been realized. Because a non-returner possesses meditative concentration (dhyāna) at the level of the first dhyāna or above, after death they are reborn among the five Pure Abodes (ākṛtāvāsa) in the form realm to continue cultivating the path, where they attain the fourth fruit of arhatship and directly enter nirvāṇa without remainder (anupadhiśeṣa-nirvāṇa), never returning to the human world again; 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, or the third fruit. Therefore, one must not believe that there is truly a fruit of the non-returner to be attained, must not believe that a third-fruit person truly exists as a real entity, and must not give rise to grasping (upādāna) or pride. If one does, one is not a third-fruit person.