Why SSB is a form of amplitude modulation in which the balanced modulator removes the carrier and a filter (or phasing network) removes one of the two redundant sidebands, so all transmitter power goes into the single remaining sideband carrying the voice information. That makes it roughly a third the bandwidth of full AM (about 3 kHz versus 6 kHz) and far more power efficient, since no energy is wasted on a carrier that carries no information. Both sidebands contain the same audio, so discarding one loses nothing.
Watch out The choice that keeps the carrier describes single sideband with reduced or full carrier, which is not standard amateur SSB; ordinary double sideband AM keeps the carrier and both sidebands. The choices about SSB being the only authorized voice mode are simply false, since AM, FM, and digital voice are also permitted on HF phone segments.
SSB = Suppress carrier, Suppress one Sideband. One sideband survives, that's all.