Water swirls because it’s the course of ‘least action’ for the draining process. It creates a laminar and continuous volume exchange through a hole. Pipes are usually filled with air which has to be exchanged with water to drain. Physics just optimizes itself to be as efficent as possible with this. You can’t have a perfect draining surface so so currents in one direction will always be a little bit stronger that in the others. Gravity applies a constant acceleration, so this small difference in initial direction will be amplified over time creating a swirl.

In case of a toilet though, the water is already introduced in a swirl during flushing. So none of the above even matters.