Why do bikes hardly ever skid while braking with the front wheel?

Because, when you brake, your weight is being shifted towards the front wheel. The inertia coupled with gravity puts your weight and that of the bike onto the front wheel. More weight ⇒ more pressure ⇒ more friction/grip with the ground.

In addition to Alex Doe's answer: front wheel drift does occur on slippery surfaces, Unfortunately a bike is really unstable in this mode so you'll fall over very soon (whereas a rear wheel drift is pretty stable and controllable).

Why rear wheel easily drifts?

Consider the torque around contact of front tire from the frame of the cycle.

• The pseudo force on the rider and the cycle is in forward direction

• Thus, the weight and thus the normal force on rear tire tends to decrease.

• Thus smaller friction force and bicycle tends to drift.

Why front wheel rarely drifts?

• Considering the pseudo force and the tendency to rotate, the normal force on front tire is much larger (due to forward pseudo force on the centre of gravity). Thus, the grip is very tight.