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” — corresponding to the sin.
Diyuk of “al chatato asher chata” — the offering must match the specific liability created by the sin.
The animal (and its designation) is brought as the counterpart to the particular chatas/asham obligation that arose from the sin in question. The verse’s language “for his sin which he sinned” requires a precise correspondence rather than a generic offering that could serve any liability.