Op-amp inductive output impedance oscillation
The rising Rout also contributes a phase shift.

That internal-to-opamp phase shift interacts with the external capacitor to produce a total of 180 degrees.

The unwanted 180 degrees, along with the opamp's negative close-loop gain, becomes 360 degrees.

And Barkhausen tells us ........



Here is a simulation you could be running; the lower left plot shows the virtual inductance.

The upper left plot  shows the 30dB peaking, where XL = Xc (the 1uF cap).



Notice, in the upper plot, the 30 db peak frequency is 40KHz..

Then examine the lower plot, and find the reactance is 4 ohms (J*4 ohms).

Now..... what is the reactance of 1uF capacitor at 40,000 Hz?