If a piece of skin from a neveilah (animal carcass) had been removed from the animal but still had a kezayit (olive-sized amount) of meat on it, and somebody touched a tiny piece of meat sticking out—not the actual part of the meat, but a piece protruding outward—or a hair on the skin on the opposite side of the meat, the skin side, the person is tamei (ritually impure). The thin piece of meat sticking out is the yad; it's like part of the handle of the meat. The hair on the skin side is considered to be part of the shomer, part of the protector of the meat. Therefore, the yad and the shomer can pass tumah (ritual impurity) from the meat to the person who touched it.
If there are two separate half-kezayit pieces of meat on the skin of a neveilah, according to Rabbi Yishmael, the tumah transfers through carrying the whole piece, but not through touching it. This is the opinion of Rabbi Yishmael. When a person is carrying it, since there are two halves of a kezayit, he is carrying a full kezayit with one action. It doesn't matter that the pieces are broken up into two sections. Therefore, the tumah transfers through masa, through carrying it. But touching it requires two different fingers or two different hands, which is considered to be two different actions of touching. Therefore, both pieces are less than a kezayit, and the tumah would not transfer through maga (touching it). This is the opinion of Rabbi Yishmael.
Rabbi Akiva omer (says): lo be-maga ve-lo be-masa—not through touching it or through carrying it. The two half-kezayit pieces of meat cannot make a person tamei. Each piece is less than a kezayit, so they are batel, they're insignificant, and, like the part of the skin, which has no tumah of the neveilah, they're not one entity. Therefore, even though the person is doing one action of carrying them, they have to be connected. So even for masa, according to Rabbi Akiva, there is no transfer of tumah. We'll elaborate on Rabbi Akiva's view.
He would agree with Rabbi Yishmael's opinion regarding the two half-kezayit pieces of neveilah meat that were not attached to the skin: once someone stuck them together with a toothpick and then moved them, he carried a full kezayit of neveilah. When the toothpick is connecting them, they're considered to be one entity. Even though they're not touching, there is a bridge between them—the toothpick—and they're considered to be like a full kezayit.
Why, then, does Rabbi Akiva say that the case of or, the skin, where there are two half-kezayit pieces attached to the skin, is pure? Shouldn't that be similar to the toothpick case, where there's a bridge between them? Why not let the skin act as the bridge between them as well, and say that the person would be tamei in that case too? The Mishnah answers: What is Rabbi Akiva's rationale? Rabbi Akiva says that the skin they're attached to nullifies them, and each piece is considered to be less than a kezayit. In other words, since they're part of something else, when they're part of something else, they're not considered to be the most chashuv (important) part of it. There's a bitul, there's a nullification that happens. Even though they're both attached to the same piece of skin, the meat is not the main component of the skin, and therefore the pieces are nullified to the skin. Therefore, no tumah would transfer, because they're attached to the same piece of skin, and therefore they're nullified to the skin, and therefore no tumah would transfer, because they are two individual pieces and both are less than a kezayit.