How does an inductor generate back emf equal to a source driving it?
One way to think of a inductor from the circuit's point of view is that it gives inertia to current.  This gives you some intuitive feel for why current builds up slowly as voltage is applied, and why the voltage goes as high as it needs to on a attempt to shut off the current abruptly.  This isn't how the physics works, but this can be a very useful mental model for understanding and designing circuits with inductors.