Why do you need to take out your laptop from your bag during airport security checks?

Generally it's so that they can check the metal device that it is, and that nothing else is hidden in it. Same with SLR cameras on occasion, and I've been asked in the past to turn both of them on to prove they actually work. But generally they just want a clear and unobstructed view of all the workings, especially to see the harddisk platter. That caused some problems when SSD drives came out and they couldn't see any moving parts...

The TSA has just approved "Checkpoint Friendly" Laptop bags :

To help streamline the security process and better protect laptops, TSA recently encouraged manufacturers to design bags that will produce a clear and unobstructed image of the laptop when undergoing X-ray screening. A design that meets this objective will enable TSA to allow laptops to remain in bags for screening.

British authorities don't seem to explain much either in general, but do require that they are screened separately:

Laptops will need to be removed from your bag at Heathrow Airport and screened separately in the trays provided.

The innards of a laptop are confusing enough on their own but when you then overlay that image with the shadows cast by the accessories it turns into a confusing mess they can't understand.

Any such confusion of items will likely draw an inspection. They are just pre-empting it by saying to take the laptop out. It's also why they recommend you arrange electronics in a single layer in your carry-on--they're trying to avoid the confusion that necessitates a search through the bag.