The Gemara establishes the Halachic principle of "Ein Ma'avirin Al Ha'mitzvot," which means that one should not pass over a Mitzva opportunity without fulfilling that Mitzva. If one has before him two Mitzvot to perform, he should first perform the one that he comes upon first, rather than letting it pass so that he can first perform the second Mitzva. Tosafot appears to have understood that this principle constitutes a Torah law, and not merely a Rabbinic enactment.
A daily application of this rule involves the arrangement of one's Tallit and Tefillin in his "Koracha" (bag). Halacha requires that one first don his Tallit before donning his Tefillin. However, if one's Tefillin is positioned on top of the Tallit, such that when he opens the bag he first encounters the Tefillin, he will have to pass over the Tefillin in order to first wear his Tallit. One must therefore ensure to position his Tallit and Tefillin in such a way that he will not first encounter the Tefillin. The Ben Ish Chai (Rabbi Yosef Chayim of Baghdad, 1833-1909) writes that the Tallit and Tefillin should be positioned side-by-side, since the sanctity of the Tefillin exceeds that of the Tallit, and thus the Tallit should not be placed on top of the Tefillin. Instead, they should be placed next to one another, and the Tallit should preferably be placed at the side where one's hand is situated when he finishes opening the zipper.
If one mistakenly removed his Tefillin from the bag before his Tallit, which should he wear first? Should he first put on his Tefillin to avoid transgressing the rule of "Ein Ma'avirin Al Ha'mitzvot"?
The Shulchan Aruch (25) writes explicitly that in such a case one must, indeed, first wear his Tefillin. The Arizal and other Kabbalists, however, held that the Tallit must always be donned before the Tefillin, even if it means passing over the Mitzva of Tefillin to first wear the Tallit. This is the ruling of Rabbi Chayim Palachi (Rabbi of Izmir, Turkey, 19th century) as well as of the Ben Ish Chai. Chacham Bentzion Abba Shaul (Jerusalem, 1924-1998) followed the view of the Kabbalists, whereas Chacham Ovadia Yosef advocates following the position of the Shulchan Aruch. Common practice seems to follow the ruling of the Kabbalists, that even if one mistakenly took his Tefillin before his Tallit, he should first don his Tallit before putting on his Tefillin. One can avoid this problem by putting down the Tefillin and stepping out of the room for a moment, diverting his attention from his Tefillin. When he returns, he may then take his Tallit and wear it first according to all views.
Summary: One must not place his Tefillin on top of his Tallit when putting them in their bag; instead, the Tallit should be positioned next to the Tefillin, preferably to the side where one's hand is situated after he opens the bag. If one mistakenly removed his Tefillin from the bag before his Tallit, then some views require that he first don his Tefillin, whereas others maintain that he should first wear his Tallit; common practice seems to follow the second view, that even in such a case one first dons the Tallit. A person in this situation is advised to put down the Tefillin, leave the room for a moment, and then return, so that according to all views he should now first wear his Tallit. (See Or Ltzion, Helek 2)
