Can someone explain me that when we sample that sinusoid with a frequency below the Nyquist frequency (below half the sampling frequency), why we end up taking two samples per cycle of the sinusoid?
Nyquist gives you the minimum sampling rate so that you can determine the frequency of a periodic wave.
If you sample a sine wave at 0.75 Nyquist, you get a false sine wave as shown in black dashes. This is called aliasing and it occurs at any frequency below Nyquist.
At Nyquist, you can determine frequency, but not amplitude, of a sinewave as shown by the black dashes.
Almost all images of Nyquist on the web show sampling at the peak, which is almost impossible. The following is a more appropriate representation.
Above Nyquist, it is possible to see frequency and amplitude of a periodic waveform by repeated samplings. At 1.25 Nyquist: