How is a human whistle a pure sine wave?
This is only an approximation!


While the sound of whistling has a very prominent first harmonic, the other harmonics are still present too; there's a non-harmonic noise component; and the first harmonic is more a narrow bump than a sharp line. A better description of the sound of whistling would be white noise filtered through a band-pass filter with a very high Q, and sent through a slight waveshaper adding harmonics. With a slight modulation of amplitude and filter frequency.
A pure sine wave is a  stationary signal, it has constant frequency and constant amplitude. If you observe a whistling sound on a window larger than a few tenths of seconds, you will observe modulations in frequency (because of the melody and articulations between notes), and modulations in amplitude (as you breath and start/end notes).