However, a double pole breaker is used with a typical 220v circuit (like for a dryer or heater) having two hot wires. If there is a short circuit to either hot wire, both poles are ganged together so both trip together.
If you fed a 220v air conditioner (just for example) with two single-pole breakers instead of one double-pole breaker, it's possible that a short to one of the hot wires would trip only one breaker, leaving the other energized. That would be very dangerous!
So, that's the main reason the NEC requires two-pole breakers for two-wire circuits.