Why does an inductor behave as a capacitor at high frequencies?
An ideal inductor would not behave like a capacitor, but in the real world there are no ideal components.

Basically, any real inductor can be though of an ideal inductor that has a resistor in series with it (wire resistance) and a capacitor in parallel with it (parasitic capacitance).

Now, where does the parasitic capacitance come from? an inductor is made out of a coil of insulated wire, so there are tiny capacitors between the windings (since there are two sections of wire separated by an insulator). Each section of windings is at a slightly different potential (because of wire inductance and resistance).

As the frequency increases, the impedance of the inductor increases while the impedance of the parasitic capacitor decreases, so at some high frequency the impedance of the capacitor is much lower than the impedance of the inductor, which means that your inductor behaves like a capacitor. The inductor also has its own resonance frequency.

This is why some high frequency inductors have their windings far apart - to reduce the capacitance.