The answer to 'why is my central air leaking water' is that the most common cause is a clogged or malfunctioning condensate drain line. When the air conditioner runs, it removes moisture from the air, which collects in a drain pan and is supposed to drain outside. If the drain line becomes blocked, the water will back up and start leaking.
Other possible causes include a cracked or damaged drain pan, a refrigerant leak, or issues with the evaporator coil. Leaks can also occur if the unit is not properly leveled or installed.