The "non-self is nirvana" argument by the Theravada (not to be confused with Theravada Buddhism of the Dhammakaya Foundation) asserts that nirvana is anâtman or non-self by the following argument.
Supported by verse 279 from the Dhammapada and a verse from Anguttara-Nikaya verse (A. i. 286), which are identical, Theravada claim that because both verses read, “All phenomena (dhammâ) are non-self (P., anattâ; S., anâtman),” and since nirvana is a dhamma, it stands to reason that nirvana must be non-self. But this fallacy, which is precisely what it is, doesn't hold water. Exposing this deception for what it is, the commentary to verse 279 of the Dhammapada states, unambiguously, that “All dhammas: sabbe dhammâ" only refers to the Five Aggregates (Carter & Palihawadana, The Dhammapada, p. 312). These aggregates are never other than dependently arisen and conditioned.
Elsewhere in another discourse the Buddha makes a distinction between dhammas conditioned or unconditioned (sankhatâ vâ sankhatâ) at A. ii. 34. There is no lumping up of constructed with unconstructed dhammas in this pericope. They are separate. In addition, Udana (28) speaks of a monk as “knowing nibbana of the self” (jaññâ nibbânam attano)—not of the non-self. The commentary (UdA, 191) does not lend any support to the claim that attano is used in a conventional sense or as a pronoun.
The most important point of all, is the Buddha tells his monks that “you should abandon desire for whatever is anattâ (SN 22:68). If the Theravadin choose to believe that somehow anattâ is nirvana, how can their belief be consistent with what the Buddha said—are the monks supposed to also abandon nirvana? Another problem, regarding the expression, all dhammas, the Buddha says:
“Having transcended all dhammas (pâragû sabba-dhammânam), free from clinging he has attained nirvana” (A. i. 162).
“All dhammas” thus refers to samsara as does non-self.