Torah Temimah cites Toras Kohanim (Sifra, Vayikra Dibbura DeChovah, Section 10).
Sefaria — Toras Kohanim (Sifra, Vayikra Dibbura DeChovah, Section 10)
“For his sin which he sinned” — for that specific sin which he sinned.
Diyuk of “al chatato asher chata” — confession and offering must correspond to the specific sin.
Vidui and the oleh ve-yored are directed to the specific transgression that caused the liability, not a generic confession. A person who sinned by false oath cannot discharge the obligation by confessing an unrelated failure; the offering and the words must match the actual sin. This correspondence is what makes the atonement process coherent.