In what is considered the oldest set of canonical texts, the Pali-canon of the theravāda or southern Buddhism (Hīnayāna), the compound “offering of the self” does not occur.
We find “offering”, i.e. anukula which is an offering of something for the well-being of the group / clan / family, or country.
In spite of that an early translator of the Pali canon speaks of ātappan as offering of the self. As such it appears in the Monier-Williams dictionary which will not be revised in the foreseable future.
These early translators, mainly brought together in Oxford where they established the Pali Text Society, considered what they encountered against the backdrop of their own Christian-inspired patterns of thinking and writing.
Later generations of translators, stationed in Sri Lanka and/or working for the Wisdom Library could leave the old patterns of thought behind and correctly translated the word ātappan (from Pali: ātappa, Skr.: ātāpya) as “dedicated”, “dedication”, “exertion”, and “exertion” has the Sanskrit root “tap“: giving out heat, practicing austerity.
Practicing austerity, the Christian-inspired says, is self-mortification or offering of self. The Hindu world may agree with this interpretation, but the Buddhist world does not. In the absence of abiding or enduring self it is impossible to chastise this self into submission. Here ātappa simply means putting an effort.
There’s another word that falls under the same category: uttaraná. The same early translators as mentioned above gave it as “saved” or “rescued” as in “saved by a savior”. However, uttaraná means “crossing”(the river), or “having crossed” (the river), i.e. “having arrived at the other shore” (of enlightenment.) “Saving” in the western sense of the word is not the appropriate translation.