Halitzah in our days Deuteronomy 25:10 “And his name shall be called in Israel the house of him that had his shoe loosed. ”
Jerusalem Talmud Yevamoth chapter 12 halacha 6: “And his name shall be called … The one who says that halitzah is praiseworthy learns from similar language. It says here “and his name shall be called …”. It says there “and let my name be named in them“. Just as the calling in verse in Genesis refers to something praiseworthy, so too the calling in reference to halitzah is praiseworthy.
Torah Temimah Colloquial Translation on Note #167
It seems that the general intention of this explanation is because, at face value, the process of halitzah and calling the brother-in-law “the house of him that had his shoe loosed” appears to be derogatory in order to embarass him for not performing the leverite marriage thus not creating a name for the deceased brother as it is written: “So shall it be done unto the man that doth not build up his brother’s house. This makes sense when the man has a choice to perform halitzah or leverite marriage. By choising halitzah, he must endure this emberrassment. As we (Ashkenazim) hold today, even if a man wants to perform leverite marriage, we only allow him to perform halitzah because of various reasons. [Peraps he does not have the right intentions. There is also the injunction of Rabbeinu Gershom prohibiting one from having more than one wife. According to some Poskim, this applies even in the case of mitzvah, such as leverite marriage]. As such, it is difficult to comprehend why we publicize his degradation when, from his perspective, he prefers to perform leverite marriage. Based on this some opions hold that, in our days, the mitzvah of halitzah is preferred over the mitzvah of leverite marriage. This opion interprets “And his name shall be called in Israel” not as derogatory, rather praiseworthy as in the verse “And My name shall be called in them (gen 48:16) because this man obeys the law, performing halitzah when he would prefer to perform leverite marriage. This homily supports this by comparing the similar language of “and shall be called” to “and let my name be named in them”, which is praiseworthy. Take note.
This still does not explain why he must bear the degradation of the procedure of halitzah: the loosening of the shoe and the spitting, etc., for he does not have the fault of not performing the leverite marraige as explained. This could be a proof to the what of many of the Rishonim write that the essence of halitzah, aside from permitting the widow to marry anyone else, is a spiritual fixing of the soul of the deceased. Refer to Nachmanides, Rabeinu Bechaye and the literature of the Acharonim. Thus the crux of the question is from the publicizing aspect of halitzah rather than the procedure itself.
This homily shows the sensitivity of the halacha to the brother-in-law. At face value, the verse implies that the preferred mitzvah is leverite marriage is preferred. Halitzah is performed when the brother of the deceased does not perform leverite marriage, partly to publicize his refusal to do so and partly to allow the wife of the deceased to marry anyone else. Yet there are instances, such as a kohen gadol, where the brother-in-law is not allowed to perform leverite marriage even if he so desires. The Tractate Yevamoth discusses other instances where one may not perform leverite marriage because of a rabbinic injunction. It also discusses whether leverite marriage or halitzah is preferred. One opinion is that leverite marriage is preferred. Abba Shaul says that halitzah is preferred because most people do not have the proper intention to perform leverite marriage. Thus, no matter how the halacha rules. One is praiseworthy for upholding the halacha.
 Deuteronomy 25:10
 Genesis 48:16
 Deuteronomy 25:9
 The Shulhan Aruch allows leverite marriage. The Ramah forbids it. Ashkenazi practice follows the Ramah. Rabbi Ovadiah Yosef, Z’TL, defends the practice of leverite marriage for Sephardim.