R. Yonathan says (Devarim 6:8-9) "and you shall tie them … and you shall write them": Just as the writing (of the mezuzah (a parchment scroll affixed to doorposts)) is with the right hand, so, the tying of the tefillin (on the left hand). Abba Yossi says: We find the right to be called "hand," and even though there is no proof (for its application here), it is intimated in (Genesis 48:17) "that his father placed his right hand." And what is the intent of "upon your hand"? To include an amputee (of the left hand), that his tefillin are placed on his right arm.