Why did FAA regulations initially prevent passengers from making phone calls during a flight?
While there is a chance it can interfere with aircraft equipment there are lots of other reasons as well. 


It's disturbing, you would not want a can full of people yapping on their phones for 5 hours while others tried to sleep. Lets be honest does asking someone to "Keep It Down" ever really work. 
It's very taxing on the cell network itself. Without going into lots of detail about how cell phones work, the short and sweet of it is that when you are moving (say in a car) your phone is constantly hopping form tower to tower. At the speeds a plane moves at you would hop tower at a rate that would be far more taxing on the system than when you are in a car and could lead to dropped calls and other connection issues. 
You need to listen up! While the laws on in flight entertainment have become more relaxed over time, one of the reasons you are not to use things during takeoff and landing is these are critical times in the flight (for something to go wrong) and if it does, you need to be attentive and able to listen to instructions. This, on some level, holds true for the whole flight as well I would think.
The phone itself occupies its own frequency band outside of the band that aircraft radios use however there is always a possibility when you have 2 EM waves that interference will occur.