Why do I need an 8 gauge cable for 40 amps at 220v?
No, it’s 40 amps on each wire. The current flows from one hot, through the loads, and out to the other hot and is the same current all of the way. You may be thinking of voltage. Each hot terminal is only 120. volts to neutral or ground. In theory, you could use insulation on the wires that is only rated for 120 volts but insulation is cheap.