why 3 phase?

This subject has been well covered in a recent thread, the only known use for 6 phase (3 phase/bi phase) is when the AC supply is converted to DC for long distance transmission through submarine cables.

Economic convenience.

1 Phase is inefficient, but only requires 2 wires. Polyphase power in multiples of 3 uses fewer wires. Wires, and the labor to install and maintain them, costs money.

2 phase is better than 1 phase, but needs 4 wires.

3 phase is better yet, and only needs 3 wires.

4 phase would need 8 wires

6 phase would need 6 wires

Etc. etc, etc.

Most of our long distance high voltage power transmission (400KV) uses three phase/bi phase with six wires on towers plus a ground wire.

This leads to symetrical loading on the towers, doubles the transmission capacity and adds little to the cost.