With which hand should the Tefillin be removed?
[Although in general one is required to use his right hand for all matters of a Mitzvah, and the removal of the Tefillin is also viewed as a Mitzvah, nevertheless] some Sages were accustomed to remove the head Tefillin with their left hand. [Practically, one is to follow this custom. The above is only regarding the head Tefillin, however, the arm Tefillin, is obviously to be removed with the arm which is not strapped, which is the right arm by a righty].
The head Tefillin is to be removed with one’s left hand.
With which hand should a lefty, or one who is mixed handed, remove his head Tefillin?
One whose left hand is his stronger hand should use his right, and weaker, hand to remove his head Tefillin. This applies even if he writes with his right hand and therefore wears his Tefillin on his left arm, if in truth his left hand is his stronger hand. [Thus, in general a lefty who wears his Tefillin on his right arm is to use his right hand, which is his weaker hand, to remove the head Tefillin. If, however, in truth his weaker arm is his left arm, and he just happens to put the Tefillin on his right arm due to that he writes with his left hand, then he is to remove his Tefillin using his left, non-Tefillin hand, just as is done by a righty. Likewise, although in general a righty who wears his Tefillin on his left arm is to use his left hand, which is his weaker hand, to remove the head Tefillin, nevertheless, if in truth his weaker arm is his right arm, and he just happens to put the Tefillin on his left arm due to that he writes with his right hand, then he is to remove his Tefillin using his right non-Tefillin hand, just as is done by a lefty.
Arm Tefillin: The arm Tefillin is obviously to be removed with the arm which is not strapped, which is the left arm by a lefty.
 Admur 28:5; M”A 28:3; Elya Raba 28:4
 See Admur Kama 2:3-6; Basra 2:4 that one is to always give precedence to his right over his left for all matters. The reason for this is because the right is given greater significance throughout the entire Torah regarding [the Temple service], the inauguration procedure , the Metzora purification procedure, and by Chalitza; See Beir Moshe 2:1-3 and Sefer Dinei Iter for a long list of matters that one is to do with his right hand and how a lefty is to do them.
 See Admur 28:3 regarding the different Halachos involved in the order of removal which thus relates even the removal to a Mitzvah; See also Admur and Michaber, and commentaries on Chapter 29 in which we rule to negate the opinion of saying a blessing upon the removal of the Tefillin. Now, from the fact that this negation is needed, it implies that there is at least a slight Mitzvah involved in doing so.
 Maharash of Lublin, the Rebbe of the Shlah brought in Emek Habracha 2:15; Shlah Miseches Chulin
 The reason: As the left hand is the weaker hand, and by using it one shows that it is [emotionally] difficult for him to remove his Tefillin, as in truth its Mitzvah applies throughout the day, and it is only due to that we do not have clean bodies that we remove it immediately after Davening. [Admur ibid; Shlah ibid; M”A ibid]
 Soles Belula 25:10; Machazik Bracha 28:10; Shalmei Tzibur p. 42; Zechor Leavraham 1 Taf; Chesed Lealafim 28:6; Kaf Hachaim [Falagi] 10:40; Kitzur SHU”A 10:20; Ben Ish Chaiy Chayeh Sarah 10; M”B 28:6; Kaf Hachaim 28:8
 P”M 28 A”A 3; Machatzis Hashekel on M”A ibid; M”B 28:6 regarding a lefty; Kaf Hachaim 28:8; Sefer Dinei Iter 5:8
 The reason: As the entire reason for why a right precedes the left arm is due to it being the weaker arm of the righty, and hence it would apply that by a lefty whose weaker arm is his right arm, then the Tefillin is to be removed with his right hand. Thus, even those Poskim who rule based on Kabalah that a lefty follows the same rule as a righty regarding all matters of the right versus left [See Shaareiy Teshuvah 2:2 in name of Bechor Shor page 111; M”B 2:6 regarding wearing the right shoe first; see also regarding washing hands and see there Peri Megadim 158 A”A 1; M”B 4:22 in name of Artzos Hachaim; Amudei Hashulchan 2:2; Kaf Hachaim 4:35; Miasef Lekol Hamachanos 4:53; Beir Moshe 2:1; Piskeiy Teshuvos 2:4;], this only applies in cases where the intent of using the right arm is to overpower the side of Chesed, however here that the intent is simply to show one’s hesitation to remove the Tefillin, obviously a lefty is to use his weaker arm which is the right arm, and is the opposite of the righty.
 See Admur 27:9-10 [wear on left]; Tzemach Tzedek O.C. 4:2 [wear on right]; See Piskeiy Teshuvos 27:12-15 for all opinions; Yagdil Torah 38:36 that the custom is like Admur ibid to wear on left [So ruled the Alterer Rabbanim of Anash: Rav Gringlass; Rav Shnear Zlaman Gerelik; Rav Yaakov Landau; Rav Perlow, Rav Hillel Pezner; and so rule of Rabbanei Anash today: Rav Y.S. Ginzberg]; See Igros Kodesh 11:148 regarding that some wear also on right after Davening; There is a Maaneh of the Rebbe to an individual regarding this matter, that one should follow Rabbanei, and Ziknei Rabbanei Anash, who rule like Admur ibid; See also Nesivim Bisidei Hashlichus 1:44
 P”M ibid; Machatzis Hashekel ibid; Kaf Hachaim ibid; omitted in M”B ibid; See Yeshuos Yaakov 28/1