The Midrash questions why the Torah has to specify that a Kohen becomes impure both for his deceased father and deceased mother. Why not just write his mother? It says:
[ד] יאמר "לאמו", מה תלמוד לומר "ולאביו"? מה אמו --שהיא מתחללת-- הרי הוא מטמא לה, אביו שאינו מתחלל אינו דין שיטמא לו?! אילו כן הייתי אומר מה אמו בידוע אף אביו בידוע. אביו חזקה מנין? תלמוד לומר "ולאביו".
4) (21:2) ("Only for his flesh that is near to him, his mother and his father, his son and his daughter and his brother.") "Let it be written (only) "to his mother." Why need "to his father" be written? (i.e., it can be derived a fortiori), viz.: If he makes himself tamei to his mother, who becomes a challalah (by relations with one who is unfit), how much more so should he make himself tamei to his father, who does not make himself a challal thereby! __ If so, I would say: Just as his mother is definitely known (to be his mother), so his father must be definitely known. Whence would I know (that he makes himself tamei for him even when he is known as) his father by common acceptance? It must, therefore, be written "to his father."
It's saying I would have a hava amina he becomes impure only for his mother, who is for sure his mother. But we don't know for a fact who is father is, so maybe he shouldn't.
The problem is, if his father isn't his father, then he's not a Kohen. So what's the hava amina not to become impure? A non Kohen can become impure for anyone...