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Instructor’s Response:

The third touch is important in that it confirms the validity of the line. The first point is, after all, just a random spot on the chart. The second point can be connected to the first but means nothing relative to a trendline since the second point could be anywhere on the chart and still be connected to the first with a straight line. With the third point however, if it extends the line created by the first two, now we have something that we can use.  When three points can be connected by a straight line that is confirmation of the trendline (by that third touch) and means the line can be used for trading purposes.
Take a look at the chart below for a visual...
chart 5 27 10