Why A balanced modulator multiplies the audio and carrier and cancels the carrier itself, leaving double sideband suppressed carrier (DSB-SC). A sharp crystal or mechanical filter then removes one of the two sidebands, leaving single sideband. This is the classic filter method of SSB generation; the other standard approach is the phasing method, which uses two balanced modulators fed with signals 90 degrees apart so one sideband cancels.
Watch out A reactance modulator varies the frequency or phase of an oscillator, so it produces FM or PM, not SSB. A product detector is a receiving stage that recovers audio from an SSB or DSB signal, not a generator.
Balanced modulator kills the carrier, filter kills a sideband. Reactance modulator means FM, not SSB.