Chabad.org — English translation + Rashi
Torah Temimah (Pesachim 90b): one does not slaughter and sprinkle for one who is tamei from a sheretz; the verse specifies “tamei la-nefesh.”
English: And one does not slaughter and sprinkle on behalf of one who is tamei from a sheretz. … Rather, according to Rav, even by Torah law he is not fit, for it is written: “A man, a man who becomes tamei by a nefesh.”
Limitation of the deferral — only corpse-tumah (and the parallel long-journey case) triggers Pesach Sheni.
Not every form of tumah opens the second-month path; the Torah names the specific impurity.