Why Filter bandwidth is defined between the two frequencies where the response has dropped to half the power of the peak, which is 3 dB down in voltage terms (0.707 of peak voltage). The span between that lower half-power point and the upper half-power point is the passband width. This same -3 dB convention defines bandwidth for resonant circuits, amplifiers, and receiver IF filters.
Watch out "Cutoff and rolloff" sounds plausible because cutoff frequency is a real term, but rolloff describes the slope of the skirts outside the passband, not a single defining frequency; the cutoff frequency itself is simply the half-power point.
Bandwidth = the -3 dB points. Half power, 0.707 voltage, top and bottom.