modern bike chains will withstand huge NM loads (much more than even a professional cyclist can generate) without failure
a snapped chain normally indicates:
-damage to the drivetrain (a mangled chainring tooth, which deforms the chain whilst its running over that tooth)
-damage to the chain tool used to fit the chain or poor technique when using the tool(causing the side plates to deform, which will cause the chain to fail when suddenly loaded):-this is very common and can often explain repeated failures of new chains when fitted by the same bike shop mechanic or home mechanic using the same tool
-a freak event like trail debris caught in the transmission which then damages the chain or transmission components
-poor fitment, for example a chain cut too short on a single pivot suspension bike with excessive chain stretch, although typically this will snap the derailleur hanger or derailleur before the chain snaps!
-damage to the bike: a bent derailleur hanger allows the rear derailleur to collide with the rotating rear wheel, bending the derailleur and chain
riders that claim their "power" causes them to snap chains on a regular basis are somewhat confused about how much power they can output