This is somewhat two different issues. Feedback occurs whenever the system acoustic loop gain exceeds 1 (0dB). The loop gain depends on the physical relationships, environment, patterns of the devices, response of the devices, etc. Since some of these factors differ with frequency, the loop gain can also differ over frequency, this is why the system may be more sensitive at certain frequencies. The Yamaha Sound Reinforcement Handbook has a pretty good presentation on this.I think you mean resonance. In a sense, yes it is, but it's a bit more complicated than that. It's a combination of frequencies near the mic's resonant frequency put out by the loudspeakers. The mic picks up that signal, in a way amplifies it (resonance, but it's not really amplification), sends it down the signal chain to the amps, amplified once again, goes to the speakers, wash, rinse, repeat. At least that's the watered down version I was given a long time ago. I'm sure someone more knowledgeable will be along to correct me.
Therefore more open mics on stage means a greater liklihood of something feeding back.
The second issue is NOM or number of open mics. Every time you have an additional mic picking up the same signal, they combine for an increased level. So multiple mics potentially picking up the same sound raises the resulting summed level by a factor of 10log(NOM), or 3dB for two mics, 6dB for four mics, 10dB for 10 mics and so on. Since this is gain, it raises the loop gain. A system that is stable with one open mic may become unstable with additional open mics.
So muting unused channels both makes that particular path loop gain 0 (muted) and minimizes the potential additive effects of the NOM count on the overall loop gain.
FWIW, NOM can also affect the mix. If you have 8 mics run to one group and all the mics are at 0dB from the same source the resulting level for the group is +9dB, something you may have to account for in setting the board levels and gain structure. Remember that just because the input is not clipping and the output is not clipping does not mean the signal is not clipping somewhere between the two, it may be occurring before a fader at a point that is not monitored (commonly on a group, aux or matrix bus). This can even be an issue with a console's outputs, if the faders are at -20 and the levels show 0 (many consoles are calibrated such that 0 on the meters is actually a +4dB output) then that may mean that the level on the bus itself is +24dB and might be clipping.