[dsv3099i]

I agree the overall math is easier in the frequency domain, especially because you don’t know which frequencies are problematic so best to look at all of them, but I think the concept is best explained at first, in the time domain.

Here’s my attempt in a couple of sentences.

It takes time for the signal to propagate from input to output in any real circuit. If that time is a substantial fraction of the period under consideration then the input of the amplifier, which includes the feedback signal, cannot effect the output before it has moved. And if the delay through the amplifier is just wrong relative to the signal period one can end up in a dog chasing its own tail situation and the output oscillates.

The rest is just math. :)

P.S. this explanation also explains why we use phase and not seconds to measure the delay of the circuit. Because everything is relative to the input signal period and if we use phase we get that for free. No extra divide.