A bike turns when you turn the front wheel, and the front wheel only turns in the direction it's aligned in. The pedaling motion provides a force in the up, or +Y direction. If the wheels are aligned up, the bike moves along +Y. If the front wheel is turned 90 degrees, the bike won't move. If you turn the wheel 45 degrees to the right, the bike turns to the right. But if the wheel is aligned 45 degrees to the right, that means the wheel can only turn along that direction, meaning there must be forces in both the +X and +Y direction to turn that wheel. But where is the +X force coming from? Pedaling provides force in +Y, so even if the wheel is turned, friction works against the wheel in the -Y direction, so what is pushing the front wheel with a force in the +X direction? Some thoughts: leaning when turning the bike would provide a force in the required direction. But that leads me to assume that if there is 0 lean on the bike, then the bike won't move if the wheel isn't aligned straight, because if the wheel is turned, it must need some X force to turn the wheel in that direction, and if pedaling provides force in only +Y, then there is no way to obtain a force in X.