Dynamics
    The gyroscopic
    precession of the front
    wheel does not cause
    a motorcycle to
    counter steer.
    Motorcycles counter steer because they fall over
    when you apply steering input. That is it. When
    you turn one way the bike falls the other way
    because of lateral acceleration, period. The
    reason that it falls is because it is laterally
    unstable(there is nothing mechanically holding it
    up). The fact that bikes fall over when you steer
    them is the basis for understanding why
    motorcycles behave the way that they do.

    Motorcycles counter
    steer at all  speeds.
    Some people believe that the gyroscopic
    precession of the front wheel takes effect once a
    certain speed is attained. There are only two
    ways to hold a motorcycle up, mechanically
    (your leg or kick stand) or via lateral
    acceleration. At low speeds and steep lean
    angles lateral acceleration may not be sufficient
    and  steering to full lock may not generate
    enough lateral acceleration to hold a machine
    up. At this point the machine will fall to the
    ground unless you hold it up. Counter steering
    will work as long as it can produce sufficient
    lateral acceleration to overcome gravity. As long
    as you are not trying extreme lean angles you
    can counter steer almost to a complete stop. If
    you are not counter steering then you are
    holding it up mechanically. At low speeds the
    bike does not run out of gyro precession, it runs
    out of lateral acceleration.
    What causes some of the confusion is that at low
    speed and modest lean angles the front wheel
    steers in the direction of the turn a noticeable
    amount. What proponents of this theory are
    missing is that the front wheel points into the
    direction of travel at all speeds. If this is not true
    than it makes no sense to even speak of  
    steering at all.
    Why motorcycles
    highside
    Because they are laterally unstable. When the
    rear tire looses traction in a  turn it will cause the
    bike to get sideways in relation to the path of
    travel due to inertia (the mass tries to continue in
    a straight line). While the rear has lost traction
    the front tire continues to hold the line. This is
    why the bike does not immediately low side and
    why the chassis becomes more upright as it
    goes farther sideways. When the rear tire
    regains traction while the motorcycle is sideways
    relative to the path of travel the bike rotates
    (changes lean angle) very rapidly. This is true
    whether the bike is traveling in a straight line or
    leaned over in a turn. It is also true regardless of
    how far the rear steps out whether it is 2 ft. or an
    1/8 in. There will be a lean angle change that
    corresponds. Slides cause oscillations because
    the lean angle change that occurred due to the
    tire regaining traction while misaligned with the
    path of travel forces a steering change due to the
    precession of the front wheel. Remember, the
    resulting lean angle change that occurs from the
    tire biting while misaligned with the path of travel
    is due to the center of gravity's lack of stability.
    The degree to which a bike is sideways and
    leaned over when traction is regained will dictate
    whether an oscillation or a highside will be the
    result. A highside occurs when an oscillation
    exceeds a bikes ability to recover from the last
    sequence. A violent tank-slapper that rotates a
    bike to the point of crashing is physically the
    same as a highside.
    Clip #2 At the very start of this clip Rossi
    touches down the front wheel slightly crossed up
    in order to change lean angle. This clip
    demonstrates Rossi's genius as a rider. He gets
    the bike to change lean angle and avoids wheel
    wobble by touching the wheel down only briefly.
    Notice how rapidly the bike changes lean angle
    and how quickly it slows down but continues to
    change lean angle as he carries the wheelie.
    Before the front wheel can get back off the
    ground precession straightens out the front
    wheel which slows the rate of change. As he
    carries the wheelie it is evident that he is still
    applying pressure at the bars. Even though he is
    carrying a wheelie the bike is still changing lean
    angle and the resulting precession must be
    resisted by the rider.
    Clip #3 In this clip the rider on the Proton
    attempts to do the same thing that Rossi did in
    the previous clip. However, he did not achieve
    all of the lean angle that he needed by the time
    that he landed the wheelie and was forced to
    steer aggressively the moment it landed. He
    also changes lean angle with his body while
    carrying the wheelie. He is able to do this
    because while the front wheel is off the ground it
    cannot change lateral acceleration. The lean
    angle change that occurs while he is carrying
    the wheelie cannot be from precession of the
    front wheel because the change began after he
    turned the wheel to the left. I am in no way
    critiquing these riders, only observing.
    Clip #4 Notice how the front wheel changes
    direction in perfect synchronization with lean
    angle change. It is not a coincidence. The
    precession is the reaction to the lean angle
    change. The two must happen simultaneously.
    In this particularly violent example notice how
    the bike is wagging. The bike is nearly
    highsiding with every wag. When the tire bites
    while misaligned with the path of travel it forces
    a rapid lean angle change. The front wheel
    responds (due to precession) by turning into the
    lean change. Again, that is why if you cancel out
    the gyroscopic force of the front wheel, wheel
    wobble is impossible
    These video clips demonstrate how
    the precession from the front wheel
    (which is a reaction to the act of
    changing lean angle) provides the
    energy for wheel wobble.
    Clip #1 Capirossi is in transition from left to right.
    His steering input changes the lean angle which
    causes precession to steer the front wheel to the
    right which causes the bike to stop changing lean
    angle. This momentarily allows him to steer back
    to the left which starts the cycle over until he
    releases pressure at the bars. Part of what
    started the wobble in this clip is that the rider
    aggressively changed steering input while the
    rear was sliding. That caused the rear tire to
    suddenly gain traction and quickly rotate the bike
    to the right. Of course that caused the front wheel
    to generate precession. The rider's aggressive
    steering input moves the contact patch forward
    when the bike is leaned over which effectively
    reduces trail. Short trail reduces steering effort at
    the expense of twitchy handling because it allows
    the rider to initiate a rapid change in lean angle.
    But a rapid change in lean angle only makes the
    torque generated by the front wheel that much
    greater. The mass of the bike changes lean
    angle with very little resistance. Because the
    rider must fight the torque produced by the
    precession of the front wheel it forces him to
    exert substantial energy to overcome an
    unnecessary force and in this instance caused a
    wobble.