Actually, they don't! Well, not always anyway.
The FAA recently issued a press release titled FAA to Allow Airlines to Expand Use of Personal Electronics. This press release allows for the use of some electronics, including iPads and similar devices, during all phases of flight,. However, it is up to each airline to change their procedures and to determine which devices can be safely used.
This is a small excerpt from the press release:
Passengers will eventually be able to read e-books, play games, and
watch videos on their devices during all phases of flight, with very
limited exceptions. Electronic items, books and magazines, must be
held or put in the seat back pocket during the actual takeoff and
landing roll. Cell phones should be in airplane mode or with cellular
service disabled – i.e., no signal bars displayed—and cannot be used
for voice communications based on FCC regulations that prohibit any
airborne calls using cell phones. If your air carrier provides
Wi-Fi service during flight, you may use those services. You can also
continue to use short-range Bluetooth accessories, like wireless
I flew on Jet Blue the day after that press release and they were already allowing iPads and similar devices as long as they were in airplane mode. Other airlines will follow soon I'm sure, but their manuals and procedures must be updated and approved by the FAA first.