Question

I don’t know if this is the right kind of thing to ask, but I simply didn’t understand something in learning the Talmudic passage about someone who frees half a slave.
Rabbi Yehuda HaNasi (Gittin 41a, near the top) says that it is possible: one who frees half his slave—he acquires freedom.
And there on 23b, they inferred from this that if someone frees a fetus by giving a bill of emancipation to its slave mother, that also works, since a fetus is considered its mother’s limb, and that is like freeing half a maidservant.
And Tosafot (s.v. “Ve-na'aseh”) asked: how did she acquire it for him, since he freed only the fetus? After all, even if he had freed all of her except for her hand, she would not have been able to acquire the bill of emancipation through that hand—and all the more so here.
First: why did they ask specifically about this detail of a fetus and a pregnant maidservant, and not ask more directly: “This is difficult—I don’t understand Rabbi Yehuda HaNasi’s view. How can it be possible to free half a slave, when he does not acquire his own document?”
Second: Rabbi Chaim Soloveitchik (Laws of Slaves, chapter 7, end of halakhah 5) answered that when a person acquires by means of his hand, it is not because his hand is owned by him, but rather because every person has the legal capacity of acquisition through his hand, etc.; see there.
I simply did not understand his answer.
I’d be happy if you could explain it in your own words—maybe then I’ll understand.