We mentioned above, that we learn from the pasuk והיו לאות על ידכה, that one should don tefillin on his weaker hand, which is the left. This is by a regular right handed person, if one is left handed then his weaker hand is the right hand, and the halachah is that he dons tefillin on his right hand. If one is neither right handed or left handed but is ambidextrous and uses both his right and left hand equally, the Shulach Aruch (27:6) rules that he should don tefillin on his left.
The Achronim (see Levush Orach Cham 27) explain, that even though for him it’s not the weaker hand as he is equally strong in both hands, in regards to other people the left hand is weaker, additionally, it’s opposite the heart, therefore, he should don tefillin on the left.
The Ramban (Yevamos 104a) rules that a left handed person can’t perform the mitzvah of chalitzah. Just like a Kohen who is left handed can’t work in the Beis HaMikdosh as he has no right hand, and the Torah requires that the right hand be used, similarly, since chalitzah must be done with right hand, if one is left handed he can’t perform chalitzah.
The question is, why don’t we say the same thing with tefillin for one who is ambidextrous. For one who is left handed there is no question, as he puts it on the right hand, and the right hand is the weaker hand, however, someone who is ambidextrous should be exempt as surely he has no weaker hand?
The Chasam Sofer (Shu”t Even HaEzer 2:71) and R’ Akiva Eiger (Shu”t Mahadura Kama 122) both answer, that if one will end up not doing the mitzvah altogether we don’t say like the Ramban, and we go after what is considered the weaker hand by most people. By chalitzah, it’s possible to do perform yibbum, and by the left handed Kohen, it’s possible for another Kohen to perform the avodah, however, when it comes to tefillin, if we
