I am trying to get my head around this so called tax discount? I...

I am trying to get my head around this so called tax discount?
I would have thought that the option cost would have been accountable along with the exercise cost and the capital gains would be the selling price minus the total cost. If you are worried about the time frame being extended by the longer period if they are exercised at full term, then exercise early and then the period is only a few weeks longer to get past a year or more, and the resulting shares are much cheaper. Of course there is more profit and so more capital gains tax. Am I a tax dunce?