Because they don't want to take any chances

Although most electronics have been proven not to interfere with most avionics/communications equipment in most common circumstances the simple fact remains that we aren't totally sure yet. As RRR said, airliners and electronics are both very complex, and we can't predict exactly what will happen in every situation.

In a visual landing with instrument assistance, a small error is unlikely to matter too much - if you're a little fast you may get a bumpy landing, or an incorrect descent rate may cause a bounce or a go-around etc, but the landing is unlikely to be off by a significant enough margin to cause a crash. If there's a small deviation in course/speed/altitude it won't matter, the pilot will simply correct it - likely without even noticing he's doing it - or nobody will notice/care. If there's a larger error the pilot will almost certainly notice ("Wait, why is the runway over there?") and fix the problem

In an instrument landing, however, a very small margin of error in course/airspeed etc, present for 20 miles while the pilot has no frame of reference to know that it's wrong, can cause a major issue, because the cumulative error can add up over time and there's no way to know it's wrong.

Chances are, your phone will make absolutely no difference to the plane. But on that one occasion it does cause a problem, 300 people may be killed in a fireball. That makes "asking you to stop playing Angry Birds for 30 minutes" a very small price to pay for a a potential life-saving precaution.

Because they don't want to take any chances

Although most electronics have been shown to be unlikely to interfere with most avionics/communications equipment in most common circumstances the simple fact remains that we aren't totally sure yet. As RRR said, airliners and electronics are both very complex, and we can't predict exactly what will happen in every situation.

In a visual landing with instrument assistance, a small error is unlikely to matter too much - if you're a little fast you may get a bumpy landing, or an incorrect descent rate may cause a bounce or a go-around etc, but the landing is unlikely to be off by a significant enough margin to cause a crash. If there's a small deviation in course/speed/altitude it won't matter, the pilot will simply correct it - likely without even noticing he's doing it - or nobody will notice/care. If there's a larger error the pilot will almost certainly notice ("Wait, why is the runway over there?") and fix the problem

In an instrument landing, however, a very small margin of error in course/airspeed etc, present for 20 miles while the pilot has no frame of reference to know that it's wrong, can cause a major issue, because the cumulative error can add up over time and there's no way to know it's wrong.

Chances are, your phone will make absolutely no difference to the plane. But on that one occasion it does cause a problem, 300 people may be killed in a fireball. That makes "asking you to stop playing Angry Birds for 30 minutes" a very small price to pay for a a potential life-saving precaution.