Why is the output of wien bridge oscillator sinusoidal?
Actually, the output of a Wien bridge oscillator is not always sinusoidal. If the gain at the critical frequency is less than 3 the oscillator will not oscillate. If the gain is more than 3, the amplitude will increase until clipping sets in. Any real Wien oscillator needs an AGC (automatic gain control) loop to stabilize its output.

Bill Hewlett developed a simple stabilization loop as part of his master's thesis. He used the thermal response of a lamp filament as a cheap and reliable sensing element, and went into business making very good audio sine wave generators in a garage rented by Dave Packard. The combination of names may ring a bell. The garage is still in existence.