Our Gemara on Amud Aleph quotes the verse in Vayikra (21:1) “Speak to the Cohanim, the sons of Aharon, and say to them, do not become defiled for a dead person amongst your people.” Because of the redundancy, “Cohanim, sons of Aharon”, the Gemara deduces that only the sons have this obligation, and not the daughters.  Thus, female cohanim are not prohibited from becoming exposed to impurities of death, and in practical halakha, can enter a cemetery.

What might be the reason for the distinction between male cohanim and female cohanos?  You could argue that since women do not serve in the Temple, they are not obligated to maintain a state of constant purity.  This is a possible explanation though they do get to eat from Terumah and sacrifices, so it is not a perfect argument.  

The Recanti on Chumash offers the following explanation: Cohanim embody the middah of chessed, in fact, this is how they are more able to activate atonement and forgiveness.  The harsh realities of death and resultant despondency and cynicism about life would disrupt that mode of thought and feeling.  This is why, a cohen may defile himself for a mes mitzvah, an abandoned corpse, because the intrinsic kindness involved overrides and neutralizes any disruption that would ordinarily arise from exposure to death.

Recanti asserts that women have a different strength and are not sensitized in this manner nor need extra protection from exposure to death, and so they can become defiled.  He also points out that when the Torah lists which dead relatives the cohen can become exposed to, it lists mother, father, son, daughter, brother, sister etc.  It is notable that the female comes first only in regard to the mother, however in the rest of the listings, the male precedes the female.  This too hints at the underlying feature.

What is this feature? I would have thought to say it seems to be represented in motherly compassion and chessed. The idea would be that women have this strongly ingrained but do not need more reinforcement by ritual. However, a reader brought to my attention that according to Kabbalah, the woman represents Middas Hadin, divine Justice and retribution. (See Zohar Noach (30). If so, the point of this is that woman are not activated in the same duties as the male Cohanim because of a difference in psychological nature. But how is it intuitive that men would  embody kindness and women justice? I am not sure. I do know we should be careful with how we assign these ideas. Aggression (which surely is male) may not be the same thing as lacking mercy and kindness. And motherly love and kindness might not rule out an aspect of judgment and retribution. I think the mystics were not referring to kindness as in nurturing, loving and caretaking, which clearly women do more than men. Instead I think they are referring to vengefulness and vindictiveness when wronged. Are men, by nature, generally more forgiving and less vindictive than women when they have been offended? This seems to be something closer to what the Recanti meant. Would people today agree to that or relate to that? It is dangerous territory to talk about differences between men and women, because talk about any differences can lead to unwarranted discriminatory attitudes. Nevertheless, it is something to think about. Aside from the nurturing and emotional relatedness that women are clearly more adept with, do they also manifest stronger judgmentalism, and less ability to forgive?