The second Mishnah in Shabbos lists a number of activities that one is not allowed to do shortly before the zman mincha because of a concern that the activity will extend longer than intended, leading one to miss out on the mitzvah. However, the Mishnah concludes that if one began one of these activities, he need not interrupt in the middle (assuming that there will remain time for him to do the mitzvah after the activity ends – the Yerushalmi goes so far to say that if he does interrupt when he does not need to, he’s a hedyot, and the Aruch HaShulchan (232:21) approvingly cites this halacha with the caveat that it does not applied if he started b’issur).
The gemara elaborates upon what is considered the beginning of these activities. For a haircut, it’s putting on a ma’apores (duster?) to protect one’s clothing. For working in a tannery, it’s putting on the apron of the tanners. For a meal, it’s loosening one’s belt (per the minhag on Bavel, where they used to do this; elsewhere, it’s washing). For judging a court case, it’s where the judges wrap themselves in preparation for the case (unless they’re already so garbed from a prior case). The last activity is entering a bathhouse to bathe or shvitz. The gemara states that the beginning of this activity is mi-she-y’areh ma’aparto heimenu – when he removes his garment. Rashi and the Ran (and the Beis Yosef states that such is also the shita of Rabbeinu Yerucham) define this as being the upper garment. This seems to be supported by two diyyukim. First, all of the other initiation activities appear to be the first act done to one’s person (when applicable) in preparation for the act in question. Second, the gemara uses the same lashon of ma’aparto to describe the garment to be removed in the bathhouse and the garment to be overlaid over one’s normal clothing during a haircut.
Notably, the Rambam (Hil. Tefillah 6) explains differently, saying that the bathhouse activity is not considered initiated until he strips entirely, so that the ma’apores is the garment directly on the flesh. What is the Rambam’s shita that leads him to say differently than the other rishonim?
The Rashash, without further comment, observes that the Rif (as well as the Ran commenting on him) has a different girsa, mi-she-ya’avir ma’arparto heimenu. Perhaps one could say that ma’avir would imply removing a single superficial layer from one’s body, while m’areh is from the root of ervah, and therefore has a connotation of stripping away the last layer and revealing the bare body. This would explain the Ran’s shita, although Rashi has our girsa of ma’avir. Nevertheless, Rashi could be explained by the diyyukim described above.
My chavrusa suggested a second answer. Removing an upper garment cannot be considered a true initiation of the bathhouse process, as people remove their upper garments for a variety of reasons (indeed, the gemara on the next daf describes how some amoraim would do so prior to davening as a means of demonstrating their subjugation before Hashem). Hence, only once he removed the bottom garment is it recognizable that he has begun.