How do crystal oscillators work with feedback consisting of CMOS inverters?
Inside the data sheet you will see the basic circuit of a CD4049. Here: -



If Vin is somewhere about halfway between Vcc and Vss, both transistors are conducting and the voltage at Vout will be neither 1 nor 0. In effect both transistors together act like a potential divider; an upper resistor and lower resistor.

This is the linear operating point of this digital circuit.

Next it should be noted that if Vin were taken slightly higher then Vout would fall to Vss much more rapidly than for the small change in Vin - this indicates that there is gain in the configuration and that it is an inverting type of gain.

Next, apply a high value resistor between output and input and the ouput will stabilize and some "halfway" voltage due to negative feedback just like an op-amp would.

Next apply an ac input to Vin via a small capacitor and resistor in series and you get an analogue AC amplifier.

Are you convinced that this type of digital gate can be made into an analogue amplifier? Here's and article showing how a CD4049 can be made into an op-amp. Below is a picture of a CD4049 being used as an AC amplifier: -



Here is the article.

All that remains to make a crystal oscillator is to provide the feedback resistor (maybe 1Mohm to 10Mohm), add a couple of capacitors and the crystal and you have an oscillator. Note that the combination of output impedance and capacitor connected to the output produce a signal that is more sinusoidal that square hence you can make an approximate sine wave oscillator.

Note also that it is this network (together with the input cap to ground) AND the crystal that produces 180 degrees phase shift.