To try to understand what is happening, I suggest that you stop thinking of reactive power as being consumed or supplied. Nett power is neither consumed or supplied by a capacitor or inductor. It is supplied in one half cycle of the AC wave and consumed in the other meaning that no net power is consumed. This is the reactive nature of capacitors or reactors as distinct to the passive resistor which consumes power on both the positive and negative half waves.
Now go back to your basic DC theory. When a step voltage is applied to a reactor it opposes the build up of current through it so the current builds up slowly to steady state governed by the RL time constant. When placed into an AC circuit it causes the current to lag the voltage. In contrast the capacitor resists change in voltage across it. You cannot instantaneously change the voltage across a capacitor without infinite current flow. When a voltage is applied to a series RC circuit the voltage instantly appears over the resistor and current =V/R flows. This charges the capacitor and the voltage across it builds up slowly. As the voltage on the capacitor rises, that across the resistor falls and as does the current. The rise in voltage (fall in current) is controlled bt the RC time constant. Thus when put in an AC circuit the current leads the voltage.
You can simply look at this in that the current slowly rises through an inductor when voltage is applied and current slowly falls through a capacitor. They perform in exactly the opposite way to oneanother. Thus application of either can be used to counteract the effect of the other but neither consume of supply real power. Saying that inductors consume reactive power and capacitors deliver it is only another way of saying the they do the opposite to each other.