Why does furnace freeze?

The coil you are referring to is the evaporator, it is inside the air-handler, which also contains the heater. The evaporator freezes up when the air conditionong system is low on refrigerant. What happens, is that since the refrigerant is low, it expands more than normal which cools the evaporator more than it is designed to. As the air passes throught the evaporator, moisture in the air freezes on the cold evaporator fins. This will eventually turn into a block of ice, which will impede the air flow. Once the air flow is restricted, the air conditioner will not cool very efficently if at all. Remember that the air conditioner vapor system is a sealed system. The refrigerant will last forever unless it leaks out, so you need to find and repair the leak to stop it from re-occuring. Some companies will just recharge it, especially if it's a very small leak. That way, you'll have to call them again when it starts to freeze up.