Why do we learn shoes from Tefilin?

Maharal: Tefilin are on man. They are not like a garment that covers his body. Rather, they are tied to him. Also shoes are not like garments; they are tied to man. Tefilin are like a crown; shoes are the opposite - they are on the lowest part of man, below the foot. The Torah said, when man wants to tie to his body, he should tie first what is close to him. The left is closer to man - the right is stretched out, for he uses his right hand, and not his left hand [so much]. The Torah commanded to tie Tefilin on the left - "Al Levavecha." However, we put the right shoe on first, due to the right's importance - it should not be bare.

Rav Elyashiv citing R. Akiva Eiger: Tefilin is in the merit of Avraham's refusal to take from Melech Sedom "mi'Chut v'Ad Seruch Na'al" (Chulin 89a). The straps are in place of shoelaces; it is reasonable to compare them to each other.

Daf Al ha'Daf: Toras Chayim (Sanhedrin 72a) says that the Gemara obligates Mesiras Nefesh against a decree to wear [red] shoelaces, like Nochrim, for shoelaces hint to Tefilin. The Jewish custom was to wear black laces, just like Tefilin straps must be black. We find that the kingdom wanted to stop Yisrael from wearing Tefilin!

Why does one remove the left shoe first?

Rashi: This shows honor to the right.

Rav Elyashiv: This is not limited to shoes and clothing. It is also for bathing!

Are there times when one removes the right shoe first?

Rav Elyashiv #1: Since the left has precedence for tying, one unties the right first, then unties and removes the left, and then removes the right.

Rav Elyashiv #2: One who removes shoes for a Mitzvah, e.g. Birkas Kohanim, or before Yom Kipur, Lu'ach Eretz Yisrael says that he removes the right first. However, Beis Yosef (OC 2) says that removing is the completion of donning; there is no adamancy which he removes first.

Daf Al ha'Daf: citing R. M. Mandelbaum: There is no Mitzvah to remove shoes before Yom Kipur! If one was not wearing leather shoes, he need not wear them in order to remove them. R. S.Z. Auerbach said that since he removes them for Inuy , this is not reason to esteem the right and remove it first. However, if he removes shoes on Erev Shabbos to polish them or wear Shabbos shoes, he removes the right first, due to Kevod Shabbos. l

What is the law of one who bathes the whole body?

Rav Elyashiv: Also here, he bathes the head first, for it has the brain, which is most esteemed, and it is king over all the limbs.