Why have they announced to turn off phones while they are explicitly allowed?

I've heard from informal publications and from crewmembers that there are two reasons. First, the crew needs everyone's undivided attention during takeoff/landing, should things go suddenly wrong. Second, some have said it causes interference.

Based on the first answer, I've often wondered why it's okay to read a book but it's not okay to read from a tablet or computer. I think airline companies or crews just think it's a slippery slope and would rather ban them entirely than make the rules more complicated.

UPDATE:

Many (US) airlines now allow tablets to be used during takeoff/landing provided they are small enough (e.g. less than a certain weight). Check with a specific airline for details.

UPDATE (7 January 2017):

It really depends on the airline and applicable law. The "Mobile phones on aircraft" Wikipedia article has an excellent overview of this. For those of us in the USA, this excerpt from that article may be helpful:

Contrary to popular misconception, the Federal Aviation Administration (FAA) does not actually prohibit the use of personal electronic devices (including cell phones) on aircraft. Paragraph (b)(5) of 14 CFR 91.21 leaves it up to the airlines to determine if devices can be used in flight, allowing use of "Any other portable electronic device that the operator of the aircraft has determined will not cause interference with the navigation or communication system of the aircraft on which it is to be used.

With more people having smartphones, tablets, and the like, and with the increasing popularity of WiFi on airplanes, there appears to be more pressure to allow such devices on aircraft throughout the flight. Still, it appears to be up to the airline to set and enforce their own rules.

People sometimes get things wrong. Rules sometimes exist which have no purpose, either because they used to be valid, or because they are a 'cargo cult', or because it is seen as desirable to enforce some form of authority in certain situations, and it doesn't matter what form that authority takes.

People also sometimes find spurious justifications for rules which they don't fully understand or which have no justification. There is a strong resistance in certain cultures to saying 'We know that that rule is nonsense, however, we are going to insist on it anyway.' People are more likely to follow a rule with a made-up justification than a rule which is openly acknowledged to be pointless.