Why can't I hear the ringing sound when calling someone on my iPhone?

The ringing sound is a holdover from early phone systems, circa 1940’s, when all calls went over copper wires connected by operators, or later by mechanical relay switches, and its purpose was to signify that you were actually connected to central office that served the number you were calling. (You might also hear a busy signal, or a “reorder” or fast busy, meaning that the network was overloaded and had no capacity to handle your call.) The sound actually came from the central office at the receiving end. It carried over into ESS (Electronic Switching Systems) in the 1980’s as a legacy feature, simply because people expected it; there was no technical reason for it. (Just like we say we are “dialing” a number, when no one born after 1980 has ever actually “dialed” a phone). 

With the advent of landline internet call routing over cable or fiber and cellular, it is really meaningless, and some carriers have stopped providing this archaic service. But that decision is made by the carrier for the party you are calling, not your carrier.