Why does my drill bit destroy the screw head?
It is possible that there are several reasons for the screw head destruction.


You may be using an electrical tool that is not at all suitable for driving screws. Some tools designed for drilling holes are not going to offer enough torque at a low enough speed to properly drive screws. If your tool starts out with a huge burst of speed it can almost certainly lead to immediate stripping of the screw head.
You are using the wrong size driver bit for the type of screw that you have. If the screws are Philips head be aware that there are multiple sizes of drivers such as #1, #2 or #3.
You may attempting to use the wrong style of driver with the type of slot the screw. Do not mismatch the likes of Philips and Pozidrive. There may be other specialty type slots that are also similar but require the proper drive bit selection.
It may be that you are not properly aligned with the axis of the screw. Proper installation of screws with a driver requires that the driver be directly in line with the axis of the screw.
When driving screws with a power driver is in necessary to apply a pressure on the driver to properly keep the driver bit in the screw slot. Without proper pressure the bit can run out of the slot and strip the screw head.
It is possible that you did not properly prepare the medium into which you are trying to drive the screws. With many screws you will need a pilot hole in the area where the threads are to engage with the medium. If you are attaching another piece to the base medium you would want to provide a screw body clearance hole to the mounted piece. This can actually result in a stronger screw joint as well.