What are the reasons why a current is induced in a coil?

Current is not induced into a coil. It's voltage that is induced into a coil. If the coil is connected to a load, or even short circuited, then a current will flow as a result of the induced voltage -but it's the voltage, not the resulting current, that's induced!

Voltage is induced into a coil because the the changing magnetic field, due to the change in current (0 to Imax or vice versa) applied to that coil. The process is called 'self induction'.