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The Gemora cites Rish Lakish that one is not permitted to pass over a mitzvah and that is why the Kohen cleans the Altar before the preparation of the menorah for the Altar is closer to the entrance of the heichal. Rava (33b) states that we can learn from here regarding tefillin that the shel yad should be before the shel rosh. Rashi says that this is referring to the putting on of the tefillin for the arm comes before the head.
Rabbeinu Tam disagrees and says that it is referring to the removing and placing in the bag, that the shel rosh should be placed first in order that the next day, one should come into contact with the shel yad first. Rabeinu Eliyohu learns that it is referring to the touching of the tefillin during davening.
I cite those who see this as a conflict between the head and the heart.