Why is the Schmitt Trigger output fed back to the current source in NE 566 (VCO)?
The current source can be switched to operate either as a current source or a current sink.

When it sources a current the capacitor C1 gets charged, when it sinks a current C1 gets discharged.

Having a constant current results in a constant slope and produces the triangular waveform. To get a rising and falling edge the current needs to change direction.