This is a power vs. precision thing.
Arcane magic has a lot of power but limited precision. All the control comes from the user, that is why spells have to be learned. It is limited by the users ability to understand all the details involved, so destructive effects are much easier than constructive. Consider the classic fireball spell which probably works something like: set up an enclosure then open a portal to the plane of fire, siphon off a bit into the enclosure, then close the portal, transport the enclosure to the designated point, and release.
Divine magic, especially healing, uses little power but usually a lot of finely detailed work, so complex in fact that it is beyond the capabilities of mortals. What a divine caster does is trading his work (religious devotion) for a deity/superior being/immortal whatever for spells/favors/tools that she uses to carry out her tasks. The actual fiddly bits of the spell are handled the deity. This also why divine casters do not have to learn their spells, when they cast the spell they supply the power but the deity, for whom the details are trivial, who directs it. Look at the classic healing spells, they have to, as a minimum, line up and reconnect capillaries, muscle fibers, bone cracks, and nerve axons. Most of these are too small to see with the naked eye, and there are literally thousands of these to repair even in a simple cure light wounds spell.
