The non-trip situation may have been from numerous factors.
[*] Load current stayed within the tolerance of the unit's trip characteristics - like not exceeding 20 amps on a 20 amp breaker, or rising briefly to only about 40 amps, then dropping back to 20 amps,
[*} Arc fault - as mentioned by others,
[*] Faulty unit or fried contacts,
[*] exceeded the AIC of the unit - highly unlikely in Residential or without a corresponding explosion of the frame!
[*] The parallel circuitry result of two branch circuits originating from the same line / phase allowed divided current levels to flow across each breaker - so each frame only saw ½ the current level flowing.
Just thinking and typing outloud!
Now if the situation was on the above mentioned and shown FPE equipment, or possibly on Zinsco type P / FP equipment, that is the exception
No need to use trip-free type breakers if using FPE or Zinsco FP/Ps! They came factory stock as trip-free!
It's been a long time since I have flamed out towards FPE and Zinsco!
BTW, not all of the FPE or Zinsco line is like this. Only certain devices are the ones with the "Sucks For Overload / Overcurrent Protection" characteristics! Unfortunately, the ones that suck were very commonly used, which is why everyone in the trade makes so much fun of them.