Current Voltage Curve of a motor
What you are measuring is the combined characteristics of the power supply, motor-control circuit, motor and load.
The power supply has a passive impedance and likely an active current limiting feature.
Brushless motors can not operate with a DC supply without an active control circuit that, in effect, changes the DC supply to AC. That circuit has an impedance and a current-limiting effect.
The motor itself has an impedance and a back EMF that affects the current.
The fan requires very little torque to turn at a low speed. As the speed increases the torque required to turn the motor increases as the square of the speed. Torque actually delivered by the motor is proportional to current.
Dynamically, the inertia of the load also has an effect. Torque = rotational moment of inertia X acceleration.