It goes back to the nature of magic versus the divine. In a fantasy world, magic is the prevailing technology (read: science) of the day. That is under the rules for AD&D and AD&D2, until the Time of Troubles and the "wild mages", magic is learned through study, apprenticeship, and is subject to laws, rules, and its own sort of "scientific method." Wizard magic is powered by universal forces and is a naturally occurring phenomenon.
As some of our friends have said before, clerical spells are the province of the gods and granted at their whims. There is no rhyme or reason; they are empowered by a higher being.
Since spirituality and an individual's essence is often seen as the domain of priests, so too is healing and restorations. Mages have a limited command of these forces, but it is usually confined to spells such as Animate Dead or other necromantic magicks.
There are several workarounds for mages, as our friend Xyx has mentioned, but none of these spells are intended to heal someone. The added hit points and such are a side-effect of another power, not their primary purpose. Plus in very few instances (ie-Wish and Limited Wish) can HP be transferred to anyone other than the caster.
There are some other RPG systems where magic-users do have command of healing magicks. For instance, in in Palladium Fantasy RPG and Rifts, there are wizards spells which can be used to heal. PFRPG also has gods, although they are different from the gods of AD&D/D&D3. Rather than being supremely divine beings, they are super-powerful alien intelligences who can transfer some of their powers to followers. It is this subtle difference from AD&D gods (which are full deities in their own right) which enables wizards in other systems to cast healing magicks.
The inability of mages to heal is not accidental; that is not their purpose under the designs of Gary Gygax et al. While some mages may know healing techniques (ie-herbalism, holistic medicines, even basic surgery, etc.), it is priests who are responsible for magical cures.
Jesus saves! And takes half damage!
If brute force doesn't work, you're not using enough.