Unitary Gain Bandwidth tells the max frequency at small signal.
If you need a large signal, you have to make sure the output can swing fast enough.
For a sinusoidal waveform, the max rate of change in the signal is during the zero crossings. Minimum required slew rate is dictated by both the frequency and the amplitude of the output signal.
For example, if you need an amplitude of A=1V and f=1MHz, the slew rate has to be at least Smin=2πfA = 2*3.14*1MHz*1V = 6.28 V/us (the fastest swing appears during the zero crossings). Now, if you need the same 1MHz, but at an output of 10V peak to peak (so A=5V), then the slew rate of the opamp has to be at least 31.42V/us.
Notice how both signals have the same frequency, 1MHz, but because the second signal is 5 times larger, it will require a 5 times faster slew rate. An opamp with GBP 100MHz but only 10V/us SR, won't be able to output a 10Vpp at 1MHz.