The Gemora asks: What is the reason for this? The verse states regarding Pinchas’ gift of Kehunah, “and it will be for him and his children after him.” This implies that for someone to be a Kohen, his father must be clearly identifiable, something not present in this case.
In the sefer, Korban Chagigah it is written that the child would be required to honor each one of the fathers because honoring one’s father is a Biblical mitzvah, and in cases of uncertainty, we act stringently.
Reb Yosef Engel in Gilyonei Hashas asks: Why don’t the laws of nullification (bittul) apply? We should say that the majority of these men are definitely not his father, and he should therefore be exempt from honoring any of them.
He writes that perhaps the laws of bittul are not applicable by positive commandments. Additionally, he suggests that a person is regarded as being prominent, and therefore they cannot become nullified.