Why does voltage always lead current by 90 degrees in an inductor?
It's really that the current is the time-integral of the voltage, or the voltage is the derivative of the current.  If the current is a sine, then the voltage is a cosine, since that's the derivative of a sine.

The way derivatives and integrals of sinusoids work, each is &frac14; cycle, or 90&deg;, phase shifted from the next.