Why is the feedback of op-amp oscillators connected to inverting input instead of positive input
Making this as simple as possible, when oscillating one end of the inductor will be rising in voltage while the other end is falling. The current in the inductor charges one cap positively while it charges the other negatively. As those charges accumulate the current falls in the inductor till it reverses and the whole thing repeats in the other direction. The resultant see-saw in currents is what makes the whole thing ring at it's designed frequency.

Since, as I mentioned above, the voltage polarity is reversed across the inductor the op-amp needs to be connected as an invertor, i.e. using negative feedback as shown.

Note: Given an initial stimulus the circuit will ring at the oscillation frequency on it's own, with no op-amp in the circuit, till it decays due to losses. The op-amp overcomes those losses and keeps the thing ringing as long as power is applied.