Why are crystal oscillators used in clocks instead of RLC circuits?

Crystal oscillators are much more accurate, they are small, have low temperature coefficients and low drift at a low cost.

A quartz crystal is a mechanical resonator with particularly stable properties. Quartz is a very stable material -- it doesn't 'age', or change much with temperature. It is also possible to prepare quartz to be very pure and have consistent properties. Quartz is also slightly piezoelectric -- an electric field causes a deflection, and a deflection generates an electric charge.

When cut correctly (with a specific orientation w.r.t the crystal axes) and mounted correctly, the mechanical properties (basically stiffness) are independent of temperature. Contacts on the crystal mean that a mechanical vibration generates electrical charge, and when configured correctly (with an amplifier), the whole system can be made resonate at a stable frequency.

Electrically this can be modeled as a RLC network with similar properties. The RLC values may be surprising -- typically fractions of a fF of capacitance and many henries of inductance.

The reason is accuracy. For capacitors 2% is considered a very good tolerance. I'm not sure about inductors but I expect it's similar. Resistors are better than capacitors or inductors but you can't build an oscilator with resistors alone.

To put these numbers in perspective: 1% is equivalent to 36 seconds per hour or 14 minutes and 24 seconds per day, which would be totally unacceptable accuracy for a clock.