Inductor behavior when connected to inverter
As a thought experiment, if the inverter gate has a signal propagation delay of 50 ns, then, if it oscillates when you connect output to input directly, the propagation delay is equivalent to an extra 180° of phase shift. So, if \$t_P\$ is 50 ns, the inverter would oscillate at 10 MHz because 180° of the period of 10 MHz is 50 ns.
If you fed the output back via an inductor, the inductor and the input capacitance of the inverter (a few pF) will add some more delay. Maybe that delay is 10 ns. Now, that means the frequency that has half a period of 10 ns + 50 ns is 8.3333 MHz.
Thus, if an inverter can be made to oscillate when output is fed directly to input, then replacing the direct connection with an inductor will naturally reduce that oscillation frequency.