So, you are missing several factors:

1) compression ratio means that the pressure is above atmospheric - probably what you assumed with your calculation. The pressure AND temperature is also increased - something used in diesel engines so they don't need sparks...

2) the spark needs to be "big & fat" ie just breaking down to have a feeble spark is not good enough,

3) the mechanics of the combustion process also come into play here, as the initial combustion from the spark has a delay time then the flame front will progress through the fuel charge, that is why there is spark advance so that the fuel charge has sufficient time to burn during the power stroke.