We need to look at heeling a canoe.
If your boat sits in the water, level from side to side, as it moves forward, it will push an equal amount of water away from each side.
However, if you move across to one side, the boat tips.
As the boat tips, one side comes up out of the water, leaving a straighter waterline, and the other side gets more rounded as more of the side in the middle goes into the water....
As one side of the boat gets straighter, and the other curves more, only one side pushes water away, so the boat turns.