"A y'vama acquires herself through chalitza", really?

Question

The first mishnayos of Kidushin, in Sefaria's Silverstein translation, bracketed remarks omitted:

A woman is acquired in three ways, and she acquires herself in two ways. She is acquired by money, by writ, and by cohabitation.... And she acquires herself with a get and with the death of her husband.

A yevamah is acquired by cohabitation, and she acquires herself with chalitzah and with the death of the yavam.

A Hebrew bondsman is acquired by money and by writ. And he acquires himself with years, and with the Jubilee (yovel), and with monetary deduction. The Hebrew handmaid, in addition, acquires herself with signs. A "bored" bondsman is acquired by boring (of the ear), and he acquires himself with yovel and with the death of the master.

A Canaanite bondsman is acquired by money, writ, and chazakah (proprietary act). And he acquires himself by money..., and by a writ (of manumission)....

Something is funny here.

In most of these cases, the "acquires himself" is a reversal of the "is acquired". A woman becomes a wife through money, and thereafter loses that wifehood through a get (bill of divorce). A Jewish servant becomes such by the transfer of money, and thereafter leaves servitude by the passage of years.

But for a y'vama, it's different. This is someone whose husband died childless and who therefore should marry his brother. That marriage is effected, as the mishna notes, through intercourse. And it thereafter ends — well, through a get or the death of the new husband. Chalitza doesn't end the marriage: it ends the half-married state that the woman is in immediately after her husband dies. Listing it in parallel to the other "acquires himself"s is misleading; why does the mishna do it? I'd think it would say she acquires herself through get or the husband's death.

Answer 1

I'd think it would say she acquires herself through get or the husband's death.

There would be no point of writing the Mishnah this way, because it would be redundant. We already have been told that a woman becomes unmarried via a get or the death of her husband. The Mishnah is trying to tell us how status changes are effected; the status change that has not yet been explored is how a woman who is bound to her brother-in-law can get released from that bond. The Mishnah therefore tells us that that bond can be severed either by the death of the brother-in-law, or by the performance of chalitzah.

This is kind of alluded to in the comments of R. Isaiah di Trani the Elder.

Tosafot Rid Kiddushin 2a

וקונה את עצמה בחליצה האי קונה את עצמה דיבמה לא דמי לקונה את עצמה דאשה דההוא קאי אלאחר שנקנת לבעלה והאי קאי קודם שנקנת ליבמה דאי לאחר שנקנת לו בביא' הרי היא ככל הנשים ומפטרא בגט ולא בחליצה

And she acquires herself via chalitza: This "acquires herself" of a yevamah is not the same as the "acquires herself" of a woman. For that is referring to after she was acquired to her husband, while this is referring to before she is acquired to her yavam. For if [this one] was [referring] to after she is acquired to him [the yavam] via sexual intercourse, she would be like all other woman and be released with a get and not via chalitza.

Answer 2

(Edit:

Now that I reread your question it seems your question is why by the first case (and all the other ones except the Yevama one) the word "s/he" in the words "And s/he acquires herself" is referring to the person after s/he was aquired, but in the case of the Yevama the word "she" in the same words is referring to the Yevama before she was acquired.
The answers to this is:
1. that a Yevama is different then the other cases since a Yevama was already semi-acquired (see below) (before she gets aquired by the Yovom) but all the other cases not (they were either 1. free or 2. the way they aquire themselves did not change before and after they were aquired by the new person or 3. in the case of a Jewish handmade, while she was a young daughter, her father did not aquire her but always owned her)
2. The Minshna respects the brain/storage space of Jews and tries to condense (and sort) information as much as possible, even if it does not come out as perfect/beautiful/simple as if it would be in an uncondensed way)

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Original answer

understanding what is acquired should make this question answer itself

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What is being acquired?

by a wife it is the the exclusive right for marital relations (this exclusivity is protected by the potential fine of the death penalty (of both parties involved in its violation)).
(related Wife's obligation to submit to her husband for relations )

By a slave it is the right for the work of his hands, (this is right is protected by the owner having the right to force his slave to work)

(By a handmaid she is like a slave (above) and The right for the owner or his son to marry her was also aquired by her owner

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The Mishna:

A woman is acquired in three ways...

means now she (the exclusive right for marital relations with her) belongs to one man (although she (if a virgin) has the right to wait for one year to prepare herself for the first relations)

And she (a wife) acquires herself...

means is that now this right belongs to her, meaning that she can sell herself/this-right (in other words get married) to another man.

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(A Yevama by definition is:
1. Semi-aquiered (she is forbidden to marry another, and the Yavom can aquire her against her will) and
2. Semi-free (belonging to herself) (there is no death penalty for relations with others))

A yevamah is (completely) acquired...

means that while she is a Yevama she is not really acquired
since there is not a real exclusivity
since (Minshna Nedorim 10:6):
1. if there are 2 brothers the second brother can acquire her (or let her go), and
2. (even if there is only one yavom,) there is no death penalty for adultery (or rape)

she (a yevama) (completely) acquires herself...

means that now she can get married (in other words she acquired the right to sell herself/this-right to another man)

(Before she acquires herself she has a prohibition to have relations with another man, becouse of her Yevama status)

(But it is leagaly questionable if she can let another man aquire her before she completely acquires herself from being a Yevama (so we act as though he can)
So if this other man had relations with her she is forbidden for both of them)

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And he (a slave) acquires himself

Mean that he owens the money he makes

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Thanks to @user15464 and @Meir for their help with this answer